dorsal/arxiv
View SchemaOn the Fundumental Invariant of the Hecke Algebra $H_{n}(q)$
| Authors | J. Katriel, B. Abdesselam, A. Chakrabarti |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9509012 |
| URL | https://arxiv.org/abs/q-alg/9509012 |
Abstract
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 $H_{n}(q)$.
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"abstract": "The fundumental invariant of the Hecke algebra $H_{n}(q)$ is the $q$-deformed\nclass-sum of transpositions of the symmetric group $S_{n}$. Irreducible\nrepresentations of $H_{n}(q)$, for generic $q$, are shown to be completely\ncharacterized by the corresponding eigenvalues of $C_{n}$ alone. For $S_{n}$\nmore and more invariants are necessary as $n$ inereases. It is pointed out that\nthe $q$-deformed classical quadratic Casimir of $SU(N)$ plays an analogous\nrole. It is indicated why and how this should be a general phenomenon\nassociated with $q$-deformation of classical algebras. Apart from this\nremarkable conceptual aspect $C_{n}$ can provide powerful and elegant\ntechniques for computations. This is illustrated by using the sequence $C_{2}$,\n$C_{3}, \\cdots,\\; C_{n}$ to compute the characters of $H_{n}(q)$.",
"arxiv_id": "q-alg/9509012",
"authors": [
"J. Katriel",
"B. Abdesselam",
"A. Chakrabarti"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "On the Fundumental Invariant of the Hecke Algebra $H_{n}(q)$",
"url": "https://arxiv.org/abs/q-alg/9509012"
},
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