Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras

2018/02/15 by Losev, Ivan, Panin, Ivan
#16A16 #17B35 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1802.05651

Abstract

Let \mathfrakg be a semisimple Lie algebra. We establish a new relation between the Goldie rank of a primitive ideal J⊂ U(\mathfrakg) and the dimension of the corresponding irreducible representation V of an appropriate finite W-algebra. Namely, we show that Grk(J) \leqslant dim V/d_V, where d_V is the index of a suitable equivariant Azumaya algebra on a homogeneous space. We also compute d_V in representation theoretic terms.

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