Friday, October 22, 2021 at 11:00am to 12:00pm
JO 4.614, 4.614 800 W. Campbell Road, Richardson, Texas 75080
A complex reflection is an invertible linear transformation of a finite-dimensional complex vector space that has finite order and acts trivially on a complex subspace of codimension one. A complex reflection group is a finite group generated by complex reflections. Replacing “complex” with “real”, one obtains precisely the finite Coxeter groups, which in turn comprise a generalization of Weyl groups of semisimple Lie algebras. Complex reflection groups have many applications, including to the representation theory of reductive algebraic groups, Hecke algebras, knot theory, moduli spaces, low-dimensional algebraic topology, invariant theory and algebraic geometry, differential equations, and mathematical physics.
In joint work with Nathan Williams, we study normal reflection subgroups of complex reflections groups (that is, normal subgroups that are also generated by complex reflections). Our approach leads to a refinement of the celebrated theorem of Orlik and Solomon that the generating function for fixed-space dimension over a complex reflection group is a product of linear factors involving generalized exponents. Our refinement gives a uniform proof and generalization of a recent theorem of Nathan Williams.
This talk only assumes a modest background in abstract algebra and should be accessible to graduate students.
Coffee will be served at 10:30am in the alcove outside FO 2.406
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