Orbits of spherical representations and Pyasetskii duality

2025/04/05 by Shunin, Daniil
#20G05 (Primary) 14M27 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.04125

Abstract

Dual representations V and V^* of a complex connected algebraic group G simultaneously have either infinitely or finitely many orbits. Whenever the latter holds, the orbits in V and V^* are in a bijective correspondence called Pyasetskii duality. We obtain a complete description of this duality in the case of spherical representations.

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