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Manchester Algebra Seminar - Jay Taylor - University of Manchester

Dates:11 May 2021
Times:13:00 - 14:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, Current University students
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  • Department of Mathematics

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  • In category "Seminar"
  • In group "(Maths) Algebra"
  • In group "(Maths) Maths seminar series"
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Speaker: Adam Thomas - University of Warwick

Speaker: Jay Taylor - University of Manchester

Title: Invariant Bilinear Forms on Lie Algebras

Abstract: Assume a group G acts linearly on a k-vector space V. Then G acts on the space of bilinear forms on V. A standard question in representation theory asks whether G fixes a nondegenerate bilinear form on V. Equivalently, is there a G-equivariant isomorphism between V and its dual module Hom(V,k).

In this talk we consider the case where G is a connected reductive algebraic k-group acting on its Lie algebra V = Lie(G) via the adjoint representation. A result of Herpel strongly suggests that V should admit a non-degenerate G-invariant bilinear form whenever the characteristic of k is ‘pretty good’ for G. In this talk we discuss some recent work on this problem and explain some of the standard consequences of this result, due to Richardson.

Time: 1pm Place: Zoom

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Kieran Calvert

kieran.calvert@manchester.ac.uk

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