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Your search keyword '"Kirillov, A. A."' showing total 119 results
Start Over Author "Kirillov, A. A." Publisher american mathematical society
119 results on '"Kirillov, A. A."'

1. Merits and demerits of the orbit method

Author

Kirillov, A.A.

Subjects
Mathematicians -- Methods, Mathematics -- Study and teaching, Geometry -- Study and teaching, Geometrical models -- Analysis, Mathematics
Abstract

This survey is the expanded version of my talk at the AMS meeting in April 1997. I explain to non-experts how to use the orbit method, discuss its strong and weak points and advertise some open problems.

Published
1999

13. Lectures on affine Hecke algebras and MacDonald's conjectures

Author

Kirillov, Alexander A., Jr.

Subjects
Prediction (Logic) -- Analysis, Polynomials -- Analysis, Roots, Numerical -- Analysis, Mathematics
Abstract

The paper gives a review of Cherednik's results on the representation-theoretic approach to Macdonald polynomials and related special functions. Macdonald polynomials are a remarkable 2-parameter family of polynomials which can be associated to every root system. As special cases, they include the Schur functions, the q-Jacobi polynomials, and certain spherical functions on real and p-adic symmetric spaces. They have a number of elegant combinatorial properties, which, however, are extremely difficult to prove. In this paper we show that a natural setup for studying these polynomials is provided by the representation theory of Hecke algebras and show how this can be used to prove some of the combinatorial identities for Macdonald polynomials.

Published
1997

25. Quantum groups

Author

Etingof, Pavel, primary, Frenkel, Igor, additional, and Kirillov, Alexander, additional

Published
1998
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36. Introduction

Author

Etingof, Pavel, primary, Frenkel, Igor, additional, and Kirillov, Alexander, additional

Published
1998
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37. Hamiltonian reduction and geometric invariant theory

Author

Alexander Kirillov

Subjects
Combinatorics, Physics, symbols.namesake, Hamiltonian lattice gauge theory, Invariant polynomial, symbols, Covariant Hamiltonian field theory, Geometric invariant theory, Superintegrable Hamiltonian system, Hamiltonian (quantum mechanics), Mathematical physics
Published
2016
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45. Geometric realization of Kac–Moody Lie algebras

Author

Alexander Kirillov

Subjects
Algebra, Adjoint representation of a Lie algebra, Representation of a Lie group, Non-associative algebra, Killing form, Kac–Moody algebra, Generalized Kac–Moody algebra, Affine Lie algebra, Lie conformal algebra, Mathematics
Published
2016
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48. EXTENDED QUADRATIC ALGEBRA AND A MODEL OF THE EQUIVARIANT COHOMOLOGY RING OF FLAG VARIETIES

Author

Kirillov, A. N. and Maeno, T.

Subjects
Mathematics::Combinatorics, Mathematics::K-Theory and Homology, Mathematics::Quantum Algebra, Mathematics::Representation Theory, Mathematics::Algebraic Topology
Abstract

For a root system of typeA, a certain extension of the quadratic algebra invented by S. Fomin and the first author is introduced and studied, which makes it possible to construct a model for the equivariant cohomology ring of the corresponding flag variety. As an application, a generalization of the equivariant Pieri rule for double Schubert polynomials is described. For a general finite Coxeter system, an extension of the corresponding Nichols-Woronowicz algebra is constructed. In the case of finite crystallographic Coxeter systems, a construction is presented of an extended Nichols-Woronowicz algebra model for the equivariant cohomology of the corresponding flag variety., First published in St. Petersburg mathematic Journal in vol. 22 no.3, 2011, published by the American Mathematical Society

Published
2011

50. Combinatorics and geometry of higher level Weyl modules

Author

Feigin, B., Kirillov, A. N., and Loktev, S.

Subjects
Mathematics - Quantum Algebra, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), 22E67, 14M15, 05E10, Representation Theory (math.RT), Mathematics - Representation Theory
Abstract

A higher level analog of Weyl modules over multi-variable currents is proposed. It is shown that the sum of their dual spaces form a commutative algebra. The structure of these modules and the geometry of the projective spectrum of this algebra is studied for the currents of dimension one and two. Along the way we prove some particular cases of the conjectures in [FL1] and propose a generalization of the notion of parking function representations., Comment: 15 pages, LaTeX

Published
2007
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