### Seminar in Algebra, Lie Theory, and Geometry

# Thanasin Nampaisarn

### (Jacobs University Bremen)

## "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.