Integrable models through representations of the hecke algebra

1991 ◽  
Vol 360 (2-3) ◽  
pp. 613-640 ◽  
Author(s):  
Nir Sochen
Keyword(s):  
Hecke Algebra ◽  
Integrable Models

scholarly journals Identities in Representations of the Hecke Algebra

1997 ◽  
Vol 12 (24) ◽  
pp. 4425-4443 ◽  
Author(s):  
S. Loesch ◽  
Y.-K. Zhou ◽  
J.-B. Zuber
Keyword(s):  
Boundary Conditions ◽  
Correlation Functions ◽  
Lattice Models ◽  
Hecke Algebra ◽  
Integrable Models ◽  
Partition Functions ◽  
Fixed Boundary ◽  
Point Correlation

New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed boundary conditions and of two-point correlation functions in a class of lattice models. They might also help to determine the Boltzmann weights of these (allegedly) integrable models.

scholarly journals Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 779
Author(s):  
Charles F. Dunkl
Keyword(s):  
Preceding Paper ◽  
Hecke Algebra ◽  
Type A ◽  
Macdonald Polynomials ◽  
Special Points ◽  
Two Parameters

In a preceding paper the theory of nonsymmetric Macdonald polynomials taking values in modules of the Hecke algebra of type A (Dunkl and Luque SLC 2012) was applied to such modules consisting of polynomials in anti-commuting variables, to define nonsymmetric Macdonald superpolynomials. These polynomials depend on two parameters q,t and are defined by means of a Yang–Baxter graph. The present paper determines the values of a subclass of the polynomials at the special points 1,t,t2,… or 1,t−1,t−2,…. The arguments use induction on the degree and computations with products of generators of the Hecke algebra. The resulting formulas involve q,t-hook products. Evaluations are also found for Macdonald superpolynomials having restricted symmetry and antisymmetry properties.

REPRESENTATIONS OF THE HECKE ALGEBRA FOR GL4(q)

2005 ◽  
Vol 04 (06) ◽  
pp. 631-644
Author(s):  
KENICHI SHINODA ◽  
ILKNUR TULUNAY
Keyword(s):  
Hecke Algebra ◽  
Standard Basis

In this article, we explicitly calculated the values of the representations of the Hecke algebra [Formula: see text], associated with a Gelfand–Graev character of GL 4(q), at some of the standard basis elements.

INTEGRABLE MODELS OF FIELD THEORY AND SCATTERING ON QUANTUM HYPERBOLOIDS

1992 ◽  
Vol 07 (05) ◽  
pp. 441-446 ◽  
Author(s):  
A. ZABRODIN
Keyword(s):  
Field Theory ◽  
Symmetric Space ◽  
Quantum Group ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Free Particle ◽  
Compact Quantum Group ◽  
Integrable Models ◽  
S Wave

We consider the scattering of two dressed excitations in the antiferromagnetic XXZ spin-1/2 chain and show that it is equivalent to the S-wave scattering problem for a free particle on the certain quantum symmetric space “quantum hyperboloid” related to the non-compact quantum group SU q (1, 1).

scholarly journals Hecke Algebra Actions on the Coinvariant Algebra

2000 ◽  
Vol 233 (2) ◽  
pp. 594-613 ◽  
Author(s):  
Ron M. Adin ◽  
Alexander Postnikov ◽  
Yuval Roichman
Keyword(s):  
Hecke Algebra ◽  
Coinvariant Algebra
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