\U_q(sl(n))-invariant quantization of symmetric coadjoint orbits via reflection equation algebra

2001/08/31 by J. Donin, A. Mudrov
Mathematics · #math.QA

paper · pdf

published as Contemp. Math. V. 315, AMS, Providence, RI (2002) 61-80 · Replaced by the journal version, AMS LaTeX 19 pages

arxiv created 2002/12/24 · arxiv updated 2009/11/30

Abstract

We study relations between the two-parameter \U_q(sl(n))-invariant deformation quantization on sl^*(n) and the reflection equation algebra. The latter is described by a quantum permutation on \End(\Cⁿ) given explicitly. The reflection equation algebra is used for constructing the one-parameter quantization on coadjoint orbits, including symmetric and certain bisymmetric and nilpotent ones. Our approach is based on embedding the quantized function algebras on the orbits into the algebra of functions on the quantum group SL_q(n) via reflection equation algebra characters.

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