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math.RT2026
Borel-Weil factorization for super Grassmannians
Steven V Sam
This article deals with computing the cohomology of Schur functors applied to tautological bundles on super Grassmannians. We show that in a range of cases, the cohomology is a fre…
math.RT2025
Polynomial representations of the Witt Lie algebra
Steven V Sam, Andrew Snowden, Philip Tosteson
The Witt algebra W_n is the Lie algebra of all derivations of the n-variable polynomial ring V_n=C[x_1, ..., x_n] (or of algebraic vector fields on A^n). A representation of W_n is…
math.RT2025
Kostant -decomposition of homology I. Finite-dimensional representations
Steven V Sam, Keller VandeBogert, Jerzy Weyman
We give explicit, uniform formulas for the graded characters and total ranks of the Lie algebra homology of finite-dimensional representations in all classical types. In many cases…