IMSc Webinar

Kostant Kumar modules via Littelmann paths

Mrigendra Singh Kushwaha

IMSc

Kostant-Kumar modules are certain cyclic submodules of the tensor product of two irreducible integrable highest-weight modules of a symmetrizable Kac-Moody algebra.

We give, in the spirit of Littelmann, a path model for Kostant-Kumar modules in terms of Lakshmibai-Seshadri paths.

Littelmann's path model gives a generalized Littlewood-Richardson rule for decomposing tensor products into irreducibles. An analogous rule for Kostant-Kumar modules was given by Joseph under the hypothesis that the Kac-Moody algebra is symmetric. We extend this to finite type Lie algebras and use this rule to study Parthasarathy-Ranga Rao-Varadarajan (PRV) components and generalized PRV components in Kostant-Kumar modules.

This is the speaker's Pre-Synopsis seminar, to be held on Zoom.

Zoom Meeting ID: 880 2833 8424
Passcode: 693528