# Thanasin Nampaisarn

## "Tensor Representations of 𝔤𝔩∞(ℂ)"

 Date: Mon, October 31, 2016 Time: 15:00 Place: Seminar Room (120), Research I

Abstract: In this talk, $$\mathbb{C}$$ is the ground field. Let $$V$$ be a natural representation of the Lie algebra $$\mathfrak{g}:=\mathfrak{gl}_\infty(\mathbb{C})$$. Write $$V_*$$ for a restricted dual of $$V$$. The tensor representations of $$\mathfrak{g}$$ are the $$\mathfrak{g}$$-modules of the form $$V^{\otimes(p,q)}:=V^{\otimes p}\otimes V_*^{\otimes q}$$, where $$p$$ and $$q$$ are nonnegative integers. We shall describe the Jordan-Hölder constituents, socle filtrations, and indecomposable direct summands of such representations of $$\mathfrak{g}$$. This talk is based on Tensor Representations of Classical Locally Finite Lie Algebras by I. Penkov and K. Styrkas.