The Representation Type of the I-Blocks of Category O_S

ISBN-13: 9783845419831 / Angielski / Miękka / 104 str.

Kenyon Platt

Opis

Let g be a simple Lie algebra over the field C of complex numbers, with root system relative to a fixed maximal toral subalgebra h. Let S be a subset of the simple roots of , which determines a standard parabolic subalgebra of g. Fix an integral weight in h , with singular set J of simple roots. We determine when an infinitesimal block O(g, S, J) of parabolic category O_S is nonzero using the theory of nilpotent orbits. We extend work of Futorny-Nakano-Pollack, Brüstle-König-Mazorchuk, and Boe-Nakano toward classifying the representation type of the nonzero infinitesimal blocks of category O_S by considering arbitrary sets S and J, and observe a strong connection between the theory of nilpotent orbits and the representation type of the infinitesimal blocks. We classify certain infinitesimal blocks of category O_S including all the semisimple infinitesimal blocks in type An, and all of the infinitesimal blocks for F4 and G2.

O autorze

Kenyon J. Platt received his Ph.D. at the University of Georgia in 2008. His research is in the Representation Theory of Lie Algebras. He is currently an Assistant Professor of Mathematics at Snow College.