This article is cited in 1 paper

A generalized Steinberg section and branching rules for quantum groups at roots of 1

C. De Concini^a, A. Maffei<sup>b

a</sup> Dipartimento di Matematica ``G. Castelnuovo'', Piazzale A. Moro 5, 00100, Roma, Italia
<sup>b</sup> Dipartimento di Matematica ``L. Tonelli'', Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

Abstract: In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our result including the construction of a sort of Gelfand–Zeitlin basis for a generic irreducible representation of $U_q(\mathrm{GL}(n))$ when $q$ is a primitive odd root of unity.

Key words and phrases: algebraic groups, quantum groups.

MSC: 20G07, 20G42

Language: English

DOI: 10.17323/1609-4514-2012-12-3-469-495

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