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

# Aleksander Fadeev

### (Jacobs University Bremen)

## "Precoherent and Coherent Local Systems for the Orthogonal and Symplectic Cases"

** Date: ** |
Mon, November 14, 2016 |

** Time: ** |
15:00 |

** Place: ** |
Seminar Room (120), Research I |

**Abstract:**
Let \(\mathfrak{g}_n\)'s be classical Lie algebras of the same type, where the rank of \(\mathfrak{g}_n\) equals \(n\). Let \(Q=\bigsqcup Q_n\), where \(Q_n\) is a subset of the set of simple finite-dimensional \(\mathfrak{g}_n\)-modules. We denote by \(Q_n\big|\mathfrak{g}_{n-1}\) the set of all irreducible components of \(v|\mathfrak{g}_{n-1}\) for every element \(v\in Q_n\). We call \(Q\) a precoherent local system (p.l.s. for short) if \(Q_n\big|\mathfrak{g}_{n-1}\) is contained in \(Q_{n-1}\). By definition, \(Q\) is a coherent local system (c.l.s. for short), if \(Q_n|\mathfrak{g}_{n-1} = Q_{n-1}\). We say that two p.l.s. \(Q\) and \(R\) are equivalent if there exists \(n\) such that \(Q_k = R_k\) for all \(k \geq n\).