Small spherical nilpotent orbits and K-types of Harish Chandra modules

Details Small spherical nilpotent orbits and K-types of Harish Chandra modules Small spherical nilpotent orbits and K-types of Harish Chandra modules

2006-12-31

arxiv.org/abs/math/0701034v1

Mathematics

Representation Theory

8 pages

Scientific paper

Let G be a connected linear semisimple Lie group with Lie algebra g and maximal compact subgroup K. Let K_C -> Aut(p_C) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that O is a nilpotent K_C-orbit in p_C, and bar(O} is its Zariski closure in p_C. We study the K-type decomposition of the ring of regular functions on bar(O} when O is spherical and ``small''. We also show that this decomposition gives the asymptotic directions of K-types in any irreducible (g_C, K)-module whose associated variety is bar(O).

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