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2 edition of note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups found in the catalog.

note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups

Anatol N. Kirillov

note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups

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Published by Kyōto Daigaku Sūri Kaiseki Kenkyūjo in Kyoto, Japan .
Written in English


Edition Notes

Statementby Anatol N. Kirillov and Toshiaki Maeno.
SeriesRIMS -- 1481
ContributionsMaeno, Toshiaki., Kyōto Daigaku. Sūri Kaiseki Kenkyūjo.
Classifications
LC ClassificationsMLCSJ 2008/00113 (Q)
The Physical Object
Pagination8 p. ;
ID Numbers
Open LibraryOL16665050M
LC Control Number2008558316


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note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups by Anatol N. Kirillov Download PDF EPUB FB2

A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups Anatol N. Kirillov and Toshiaki Maeno Dedicated to Kyoji Saito on the occasion of his sixtieth birthday Abstract We give a description of the (small) quantum cohomology ring of the flag variety.

> math > arXiv:math/ Title: A note on quantization operators on Nichols algebra model for Note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups book calculus on Weyl groups.

Authors: Anatol. Kirillov, Toshiaki Maeno (Submitted on 3 Declast revised 11 Mar (this version, v4))Cited by: Note t hat eac h eleme nt in V determines braided deriv ations acting on B (V), some of whic h pla y a central role in the Nic hols algebra mo del for the (quan tum) Sc hu b ert.

A Note on Quantization Operators on Nichols Algebra Model for Schubert Calculus on Weyl groups. Abstract. We give a description of the (small) quantum cohomology ring of the flag variety as a certain commutative subalgebra in the tensor product of the Note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups book algebras.

Our main result can be considered as a quantum note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups book of a result by Y.

by: Dedicated to Kyoji Saito on the occasion of his sixtieth birthday We give a description of the (small) quantum cohomology ring of the flag variety as a certain commutative subalgebra in the tensor product of the Nichols algebras.

Our main result can be considered as a quantum analog of a result by Y. Bazlov. BibTeX @MISC{Kirillov04anote, author = {Anatol N. Kirillov and Toshiaki Maeno}, title = {A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups}, year = {}}.

Our model is based on the Chevalley-type multiplication formula for KT(G/B) due to the first author and Postnikov; this formula is stated using certain operators defined in terms of so-called alcove paths (and the corresponding affine Weyl group).

Our model is derived using a type-independent and concise approach. Thus, the Nichols algebra B W provides a model for the coinvariant algebra, Schubert calculus and (in the crystallographic case) cohomology of the flag manifold for an arbitrary Coxeter group W in the same sense as the Fomin–Kirillov algebras E from [FK] provide such a model for W = by: Nichols-Woronowicz algebra model for Schubert calculus 3 ‘super’ Nichols-Woronowicz algebras Λw(W), which control the noncommutative geometry of Weyl groups W, are considered.

The structure of the paper is as follows. In Section 1 we recall basic facts about Coxeter groups, their root systems, coinvariant algebras and Schubert polynomials. In other words, we construct the “Nichols-Woronowicz algebra model” for the Grothendieck calculus on Weyl groups of classical type or type G2, providing a Author: Yuri Bazlov.

Title: A Note on Quantization Operators on Nichols Algebra Model for Schubert Calculus on Weyl groups: Authors: Kirillov, Anatol N.; Maeno, Toshiaki Publication: Letters in Mathematical Physics, vol.

72, issue 3, pp. Dedicated to Kyoji Saito on the occasion of his sixtieth birthday We give a description of the (small) quantum cohomology ring of the flag variety as a certain commutative subalgebra in the tensor product of the Nichols algebras.

Our main result can be considered as a quantum analog of a result by Y. BazlovAuthor: Anatol N. Kirillov and Toshiaki Maeno. A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groupsAuthor: Toshiaki Maeno Anatol N. Kirillov.

Nichols–Woronowicz model of coinvariant algebra of complex reflection groups. A Note on Quantization Operators on Nichols Algebra Model for Schubert Calculus on Weyl groups.

a braided Hopf algebra, called the Nichols-Woronowicz algebra, to give a new mode of thought on the construction in [6]. The quantization operator on the Nichols-Woronowicz algebra and the model of the quantum cohomology ring of the flag varieties are given in [10].

The Nichols-Woronowicz algebra B(M),which is called the Nichols alge. A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groupsAuthor: Anatol.

Kirillov and Toshiaki Maeno. A Note on Quantization Operators on Nichols Algebra Model for Schubert Calculus on Weyl groups December Letters in Mathematical Physics Anatol N.

Kirillov. We give a model of the coinvariant algebra of the complex reflection groups as a subalgebra of a braided Hopf algebra called Nichols–Woronowicz algebr Cited by: 5. the theory of braided Hopf algebras, and comes up with the so-called Nichols-Woronowicz model for Schubert Calculus on Coxeter groups, has been developed by Y.

Bazlov [1]. One of the main motivations and purposes of the present paper is to construct the Nichols-Woronowicz model for the Grothendieck Calculus for classical Weyl groups and G2,as well. Weyl groups are infinite dimensional. We establish the relationship between Fomin-Kirillov algebra En and Nichols algebra B(O (1,2),ǫ⊗sgn) of transposition over sym-metry group by means of quiver Hopf algebras.

We generalize FK algebra. The characteristic of finiteness of Nichols algebras in thirteen ways and of FK algebras En in nine ways. Affine Schubert polynomials are defined by using divided difference operators, generalizing those operators used to define Schubert polynomials, so that Schubert polynomials are special cases of affine Schubert by: 1.

which means that Weyl quantization satisfies Dirac’s quantization condition up to higher orders in ~ or in other words that the algebra of pseudodifferential operators is a deformation of the algebra of symbols in direction of the Poisson bracket.

Let us now explain the concept of a deformation quantization in some more detail. Size: KB. A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups ov, Lett. Math. Phys. 72,Mar. Presentations Lefschetz property for Artinian Gorenstein algebras T. Maeno Algebraic Geometry in Positive Characteristic and Related Topics.

A Note on Quantization Operators on Nichols Algebra Model for Schubert Calculus on Weyl groups Anatol N. Kirillov and Toshiaki Maeno Letters in.

This gives a braided Hopf algebra version of the corresponding Schubert calculus. The nilCoxeter algebra and its action on the coinvariant algebra by divided difference operators Author: Christoph Bärligea. In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form ∂ + − ∂ − + ⋯ + ∂ + ().More precisely, let F be the underlying field, and let F[X] be the ring of polynomials in one variable, X, with coefficients in each f i lies in F[X].

∂ X is the derivative with respect to X. Abstract. Nichols algebras, Hopf algebras in braided categories with distinguished properties, were discovered several times.

They appeared for the first time in the thesis of W. Nichols [], aimed to construct new examples of Hopf this same paper, the small quantum group \(u_q(sl_3)\), with q a primitive cubic root of one, was by: In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ is a subgroup of the isometry group of the root ically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite reflection ctly, Weyl groups are finite Coxeter groups, and are important.

whereas the classical quantization rule would map the Hamiltonian to the operator.A nice feature of the Weyl quantization rule, introduced in by H.

Weyl, is the fact that real Hamiltonians get quantized by (formally) self-adjoint that the classical quantization of the Hamiltonian is given by the operator acting on functions by.

Let be a field. We proved here that every derivation of a finite dimensional central simple -algebra is this post I give an example of an infinite dimensional central simple -algebra all of whose derivations are usual, we denote by the -th Weyl algebra over Recall that is the -algebra generated by with the relations.

for all When we just write instead of If then is an. A note on quantization on Nichols algebra model for Schubert calculus on Weyl groups (with ) Lett. in Math. Phys. 72 () Preprint RIMS,8p. Hypergeometric generating function of L-function, Slater's identities and Quantum invariant (with ) Algebra i Analiz 17 (), no.1, Weyl Algebra and D-modules M.I.

Hartillo and J.M. Ucha 1 Introduction The algebraic D-modules theory is related with the study of modules over the Weyl Algebra. Why D-modules?, as S. Coutinho points in his splendid book [16], is a particularly easy to answer question.

Hardly any area of Mathematics has beenFile Size: KB. Nichols-Woronowicz model of coinvariant algebra of complex reflection groups Anatol N. Kirillov and Toshiaki Maeno Dedicated to Professor Shoji on the occasion of his 60th birthday Abstract We give a model of the coinvariant algebra of the complex reflec-tion groups as a subalgebra of a braided Hopf algebra called Nichols-Woronowicz algebra.

k-Schur functions and affine Schubert calculus (with Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, and Mike Zabrocki) This book is an exposition of the subject spanning k-Schur functions and affine Schubert calculus, based on lectures at the Fields Institute in Fields Institute Monographs, Volume arxiv: Show that this algebra is central and simple (imitating the proofs for the Weyl algbra in characteristc zero, for example) This means that the algebra is in fact isomorphic to a matrix algebra, for the field is algebraically closed.

Lecture 7 - Complete Reducibility of Representations of Semisimple Algebras Septem 1 New modules from old A few preliminaries are necessary before jumping into the representation theory of semisim-ple algebras.

First a word on creating new g-modules from old. Any Lie algebra g has an. The Weyl algebra can also be constructed as an iterated Ore extension of the polynomial ring \(R[x_1, x_2, \ldots, x_n]\) by adding \(x_i\) at each step. It can also be seen as a quantization of the symmetric algebra \(Sym(V)\), where \(V\) is a finite dimensional vector space over a field of characteristic zero, by using a modified Groenewold.

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange. This tag is for questions regarding to "Weyl Group", a group associated with a compact Lie group that can either be abstractly defined in terms of a root system or in terms of a maximal torus.

The Weyl algebra Modules over the Weyl algebra Francisco J. Castro Jimenez´ Department of Algebra - University of Seville Dmod School on D-modules and applications in Singularity Theory (First week: Seville, 20 - 24 June ) IMUS (U.

of Seville) - ICMAT (CSIC, Madrid) The Weyl algebra – Size: KB. Let be a field. Pdf proved here that every derivation of a finite dimensional central simple pdf is this post I give an example of an infinite dimensional central simple -algebra all of whose derivations are usual, we denote by the -th Weyl algebra over Recall that is the -algebra generated by with the relations.

for all When we just write instead of .Browse other questions tagged abstract-algebra finite-groups representation-theory lie-algebras weyl-group or ask your own question. The Overflow Blog How the pandemic changed traffic trends from M visitors across Stack.The term "Weyl spinor" can refer ebook either one of two distinct but related ebook.

One refers to the plane-wave solutions of the Weyl equation, given here. The other refers to the abstract algebra of spinors, as geometric objects, at a single point in space-time (that is, abstract spinors in zero-dimensional space-time).