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Journal Articles Proceedings of the American Mathematical Society Year : 2021

BRAID GROUP AND q-RACAH POLYNOMIALS

Nicolas Crampé

Abstract

The irreducible representations of two intermediate Casimir elements associated to the recoupling of three identical irreducible representations of U q (sl 2) are considered. It is shown that these intermediate Casimirs are related by a conjugation involving braid group representations. Consequently, the entries of the braid group matrices are explicitly given in terms of the q-Racah polynomials which appear as 6j-symbols in the Racah problem for U q (sl 2). Formulas for these polynomials are derived from the algebraic relations satisfied by the braid group representations.
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Dates and versions

hal-03808186 , version 1 (10-10-2022)

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  • HAL Id : hal-03808186 , version 1

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Nicolas Crampé. BRAID GROUP AND q-RACAH POLYNOMIALS. Proceedings of the American Mathematical Society, 2021. ⟨hal-03808186⟩
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