#### 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

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