dorsal/arxiv
View Schemaq-Krawtchouk polynomials as spherical functions on the Hecke algebra of type B
| Authors | H. T. Koelink |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9605040 |
| URL | https://arxiv.org/abs/q-alg/9605040 |
Abstract
The generic Hecke algebra for the hyperoctahedral group, i.e. the Weyl group of type B, contains the generic Hecke algebra for the symmetric group, i.e. the Weyl group of type A, as a subalgebra. Inducing the index representation of the subalgebra gives a Hecke algebra module, which splits multiplicity free. The corresponding zonal spherical functions are calculated in terms of q-Krawtchouk polynomials. The result covers a number of previously established interpretations of (q-)Krawtchouk polynomials on the hyperoctahedral group, finite groups of Lie type, hypergroups and the quantum SU(2) group. Jimbo's analogue of the Frobenius-Schur-Weyl duality is a key ingredient in the proof.
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"abstract": "The generic Hecke algebra for the hyperoctahedral group, i.e. the Weyl group\nof type B, contains the generic Hecke algebra for the symmetric group, i.e. the\nWeyl group of type A, as a subalgebra. Inducing the index representation of the\nsubalgebra gives a Hecke algebra module, which splits multiplicity free. The\ncorresponding zonal spherical functions are calculated in terms of q-Krawtchouk\npolynomials. The result covers a number of previously established\ninterpretations of (q-)Krawtchouk polynomials on the hyperoctahedral group,\nfinite groups of Lie type, hypergroups and the quantum SU(2) group. Jimbo\u0027s\nanalogue of the Frobenius-Schur-Weyl duality is a key ingredient in the proof.",
"arxiv_id": "q-alg/9605040",
"authors": [
"H. T. Koelink"
],
"categories": [
"q-alg",
"math.QA"
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"title": "q-Krawtchouk polynomials as spherical functions on the Hecke algebra of type B",
"url": "https://arxiv.org/abs/q-alg/9605040"
},
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