Manchester Algebra Seminar - Adam Brown
| Dates: | 29 March 2022 |
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| Times: | 13:00 - 14:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, Current University students |
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Speaker: Adam Brown - UST
Title: The local Langlands correspondence and unitary representations of GL(n)
Abstract: Harish-Chandra's Lefschetz principle suggests that representations of real and p-adic split reductive groups are closely
related, even though the methods used to study these groups are quite different. The local Langlands correspondence (as formulated by Vogan) indicates that these representation theoretic relationships stem from geometric relationships between real and p-adic
Langlands parameters. In this talk we will discuss how the geometric structure of real and p-adic Langlands parameters lead to functorial relationships between representations of real and p-adic groups. I will describe work in progress which applies this functoriality
to the study of unitary representations and signatures of invariant hermitian forms for GL(n). The result expresses signatures of invariant hermitian forms on graded affine Hecke algebra modules in terms of signature characters of Harish-Chandra modules, which
are computable via the unitary algorithm for real reductive groups by Adams-van Leeuwen-Trapa-Vogan.
Place: Frank Adams (and to be streamed online*)
- subject to equipment and connection
Tea and biscuits 12:45 in the foyer
Travel and Contact Information
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Frank Adams
Alan Turing Building
Manchester
