On the Fundumental Invariant of the Hecke Algebra \(H_{n}(q)\)

The fundumental invariant of the Hecke algebra \(H_{n}(q)\) is the \(q\)-deformed class-sum of transpositions of the symmetric group \(S_{n}\). Irreducible representations of \(H_{n}(q)\), for generic \(q\), are shown to be completely characterized by the corresponding eigenvalues of \(C_{n}\) alone...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 1995-09
Main Authors: Katriel, J, Abdesselam, B, Chakrabarti, A
Format: Article
Language:English
Subjects:
Algebra
Deformation mechanisms
Eigenvalues
Invariants
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The fundumental invariant of the Hecke algebra \(H_{n}(q)\) is the \(q\)-deformed class-sum of transpositions of the symmetric group \(S_{n}\). Irreducible representations of \(H_{n}(q)\), for generic \(q\), are shown to be completely characterized by the corresponding eigenvalues of \(C_{n}\) alone. For \(S_{n}\) more and more invariants are necessary as \(n\) inereases. It is pointed out that the \(q\)-deformed classical quadratic Casimir of \(SU(N)\) plays an analogous role. It is indicated why and how this should be a general phenomenon associated with \(q\)-deformation of classical algebras. Apart from this remarkable conceptual aspect \(C_{n}\) can provide powerful and elegant techniques for computations. This is illustrated by using the sequence \(C_{2}\), \(C_{3}, \cdots,\; C_{n}\) to compute the characters of \(H_{n}(q)\).
ISSN:2331-8422