Non-Levi branching rules and Littelmann paths
Freitag, 2.12.16, 10:15-11:15, Raum 404, Eckerstr. 1
Abstract: In recent work with Schumann we have proven a conjecture of\nNaito-Sagaki giving a branching rule for the decomposition of the\nrestriction of an irreducible\nrepresentation of the special linear Lie algebra to the symplectic Lie\nalgebra,\ntherein embedded as the fixed-point set of the involution obtained by\nthe folding of\nthe corresponding Dyinkin diagram. This conjecture had been open for\nover ten years,\nand provides a new approach to branching rules for non-Levi subalgebras\nin terms\nof Littelmann paths. In this talk I will introduce the path model,\nexplain the setting of the problem, our proof, and provide some\nexamples of other non-Levi branching situations.\n
The Cremona group of the real and the complex plane
Freitag, 9.12.16, 10:15-11:15, Raum 404, Eckerstr. 1
Being the birational symmetry group of the simplest kind of variety, the Cremona groups are quite large, and, depending on the ground field, rather complicated. The classification of minimal surfaces over the complex numbers and over the real numbers is not the same, and from this some differences between the Cremona group of the plane over the complex numbers and over the real numbers arise. I would like to present some of them and motivate how they are related to the classification of minimal surfaces.
Relaxed highest weight representations from D-modules on the Kashiwara flag scheme
Freitag, 16.12.16, 10:15-11:15, Raum 404, Eckerstr. 1
The relaxed highest weight representations introduced by Feigin,\nSemikhatov and Tipunin are a special class of representations of the Lie\nalgebra affine sl2, which do not have a highest (or lowest) weight.\nWe formulate a generalization of this notion for an arbitrary affine\nKac-Moody algebra g. We then\nrealize induced g-modules of this type and their duals as global\nsections of twisted D-modules\non the Kashiwara flag scheme associated to g. The D-modules that appear\nin our construction\nare direct images from subschemes given by the intersection of finite\ndimensional Schubert cells with their translate by a simple reflection.\nBesides the twist, they depend on a complex number describing the monodromy\nof the local systems we construct on these intersections. These results\ndescribe for the first time explicit\nnon-highest weight g-modules as global sections on the Kashiwara flag\nscheme and extend several\nresults of Kashiwara-Tanisaki to the case of relaxed highest weight\nrepresentations. This is based on the preprint arxiv:1607.06342 [math.RT].\n\n