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International conference "Arithmetic as Geometry: Parshin Fest"
November 29, 2012 16:30, Moscow, Steklov Mathematical Institute of RAS


Generalized Steinberg section and application to branching rules

C. De Concini

Dipartimento di Matematica, University of Rome "La Sapienza"



Abstract: Let $G$ be a reductive group with simply connected semisimple part, ${\mathfrak g}=Lie\,G$. We are going to show how a suitable generalization of the Steinberg section of the adjoint quotient $G\to G//G$ can be used to obtain information on how a generic irreducible representation of the quantized enveloping algebra $U_q({\mathfrak g})$ ($q$ is a primitive root of $1$) decomposes when restricted to the quantized enveloping algebra of a Levi factor. In the special case of $G=GL(n)$ this yields a kind of Gelfand–Zeitlin phenomenon.

Language: English


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