scholarly journals Induced Representations of Affine Hecke Algebras and Canonical Bases of Quantum Groups

2003 ◽  
pp. 115-153 ◽  
Author(s):  
Bernard Leclerc ◽  
Maxim Nazarov ◽  
Jean-Yves Thibon
Keyword(s):  
Quantum Groups ◽  
Hecke Algebras ◽  
Canonical Bases ◽  
Induced Representations ◽  
Affine Hecke Algebras

scholarly journals Canonical bases and affine Hecke algebras of type D

2011 ◽  
Vol 227 (1) ◽  
pp. 267-291 ◽  
Author(s):  
P. Shan ◽  
M. Varagnolo ◽  
E. Vasserot
Keyword(s):  
Hecke Algebras ◽  
Canonical Bases ◽  
Type D ◽  
Affine Hecke Algebras

scholarly journals Canonical bases and affine Hecke algebras of type B

2011 ◽  
Vol 185 (3) ◽  
pp. 593-693 ◽  
Author(s):  
M. Varagnolo ◽  
E. Vasserot
Keyword(s):  
Hecke Algebras ◽  
Type B ◽  
Canonical Bases ◽  
Affine Hecke Algebras

DEGENERATE AFFINE HECKE ALGEBRAS AND TWO-DIMENSIONAL PARTICLES

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 109-140 ◽  
Author(s):  
IVAN CHEREDNIK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Quantum Groups ◽  
Hecke Algebras ◽  
Two Dimensional ◽  
Conformal Field ◽  
Affine Hecke Algebras ◽  
The Difference ◽  
Zamolodchikov Equation

We demonstrate that the quantization of momenta in different two dimensional theories of elementary particles with factorizable scattering amplitudes gives the so-called degenerate affine Hecke algebras and their versions. Some connections with quantum groups(Yangians), the two-dimensional conformal field theory and representation theory am discussed. In particular, an interpretation and generalizations of the difference counterpart of the Knizhnik-Zamolodchikov equation are found by means of the particles on a segment.

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