Date:	Fri, October 17, 2014
Time:	11:15
Place:	Seminar Room (120), Research I

Abstract: The orbit structure of real forms G_ℝ of a complex semisimple group G on a G-flag manifold Z was analyzed by J. A. Wolf in [Wolf]. One of his results was that each open orbit D ⊆ Z contains a unique complex K_ℝ-orbit C₀ where K_ℝ is a maximal compact subgroup of G_ℝ. C₀ is called the base cycle and the connected component M of all its G-translates contained in D is called the cycle space of D. D and M fit into a double fibration and the associated Doubel Fibration Transform yields numerous natural unitary representations of the real reductive group G_ℝ. In this talk I will discuss which problems and obstacles arise when one tries to generalize the notion of cycle and the Double Fibration Transform to a supergeometric setting and offer some ideas on how to solve these issues.
Reference:
[Wolf] J. A. Wolf, "The action of a real semisimple Lie group on a complex manifold I: Orbit structure and holomorphic arc components," Bull. Amer. Math. Soc., 75 (1969), 1121-1237.