Some multiplication formulas in an affine Hecke algebra
Liping Wang

TL;DR
This paper derives multiplication formulas in an affine Hecke algebra of type B_2, revealing relations between Kazhdan-Lusztig coefficients and algebraic group representations.
Contribution
It provides new explicit formulas for products involving specific basis elements in an affine Hecke algebra of type B_2, linking algebraic and representation-theoretic properties.
Findings
Formulas for products involving C_{rt} and S_{lambda} in the affine Hecke algebra.
Relations established between Kazhdan-Lusztig coefficients and algebraic group representations.
Abstract
In this paper we consider the Hecke algebra associated to an extended affine Weyl group of type . We give some interesting formulas on , which imply some relations between the Kazhdan-Lusztig coefficients and representations of some algebraic groups. Here is one element in the Kazhdan-Lusztig basis of and is an element in the center of .
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Topics in Algebra
