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Groups Generated by Involutions, Gelfand-Tsetlin Patterns and Combinatorics of Young Tableaux
Abstract: "We construct families of piecewise linear representations (cpl-representions) of the symmetric group S[subscript n] and the affine Weyl group S̃[subscript n] of type [formula] acting on the space of triangles X[subscript n]. We find a nontrivial family of local cpl-invariants for the action of the symmetric group S[subscript n] on the space X[subscript n] and construct one global invariant w.r.t. the action of the affine Weyl group S̃[subscript n] (so called cocharge). We find the continuous analogs for the Kostka-Foulkes polynomials and for the crystal graph. We give an algebraic version of some combinatorial transformations on the set of standard Young tableaux."
Physics And Combinatorics, Procs Of Nagoya 1999 Intl Wkshp
This volume contains research and review papers on different branches of mathematics and mathematical physics, written by the leading specialists. Among the contributed papers are articles on: (i) multiple basic hypergeometric functions with applications to the number theory, (ii) birational representations of affine Weyl groups with applications to discrete integrable systems, (iii) algebraic geometry and Painleve VI, and (iv) combinatorics of Kostka-Foulkes polynomials.
Physics and Combinatorics 2000
The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop.
Physics And Combinatorics, Procs Of The Nagoya 2000 Intl Workshop
The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop.
Braided Differential Structure on Weyl Groups, Quadratic Algebras and Elliptic Functions
Abstract: "We discuss a class of generalized divided difference operators which give rise to a representation of Nichols-Woronowicz algebras associated to Weyl groups. For the root system of type A, we also study the condition for the deformations of the Fomin-Kirillov quadratic algebra, which is a quadratic lift of the Nichols-Woronowicz algebra, to admit a representation given by generalized divided difference operators. The relations satisfied by the mutually commuting elements called Dunkl elements in the deformed Fomin-Kirillov algebra are determined. The Dunkl elements correspond to the truncated elliptic Dunkl operators via the representation given by the generalized divided difference operators."
Physics and Combinatorics 2000
The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop. Contents: Vanishing Theorems and Character Formulas for the Hilbert Scheme of Points in the Plane (M Haiman); Exclusion Statistics and Chiral Partition Function (K Hikami); On the Spectrum of Dehn Twists in Quantum Teichmller Theory (R Kashaev); Introduction to Tropical Combinatorics (A Kirillov); Transition on Grothendieck Polynomials (A Lascoux); Generalized HAlder''s Theorem for Multiple Gamma Function (M Nishizawa); Quantum Calogero-Moser Models: Complete Integrability for All the Root Systems (R Sasaki); Simplification of Thermodynamic BetheOCoAnsatz Equations (M Takahashi); and other papers. Readership: Researchers and graduates in mathematical physics and combinatorics & graph theory."
Decomposition of Symmetric and Exterior Powers of the Adjoint Representation of Gl[subscript N].
Abstract: "A combinatorial formula and unimodality for the principal specialization of the internal product of the Schur functions are proved. The stable behavior of some polynomials are studied."
