# Manchester Algebra Seminar - Ruben La

Dates: | 9 May 2023 |
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Times: | 13:00 - 14:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, Current University students |

Speaker: Ruben La - Oxford

Title: Maximality properties of generalised Springer representations of SO(N,C)

Abstract: Let C be a unipotent class of G and E an irreducible G-equivariant local system on C. The generalised Springer correspondence attaches to (C,E) an irreducible representation rho of some Weyl group. We call C the support of rho. It is well-known that rho appears in the top cohomology of a certain variety. Let $\bar\rho$ be the representation obtained by summing the cohomology groups of this variety. Waldspurger proved a 'maximality' result for certain generalised Springer representations of Sp(2n,C). We will discuss and sketch the proof of an analogous result for SO(N,C): if C is parametrised by an orthogonal partition consisting of only odd parts, then $\bar\rho$ has a unique irreducible subrepresentation rho^max whose support is maximal among the supports of the irreducible subrepresentations of rho^max. We will also present an algorithm to compute rho^max.

Tea and biscuits 12:45 in the foyer