Seminars & Colloquia Calendar
Vertex Operators for Imaginary gl_2-subalgebras in the Monster Lie Algebra
Darlayne Addabbo, University of Arizona
Location: Hill 705 and online (see below for the Zoom link)
Date & time: Friday, 10 November 2023 at 12:10AM - 1:10PM
The Monster Lie algebra m is a quotient of the physical space of the vertex algebra V=V^{natural} otimes V_{1,1} where V^{natural} is the Moonshine module vertex operator algebra of Frenkel, Lepowsky, and Meurman, and V_{1,1} is the vertex algebra corresponding to the rank 2 even unimodular lattice II_{1,1}. In this talk, I will discuss the construction of vertex algebra elements that project to bases for subalgebras of m isomorphic to gl_2 and corresponding to imaginary simple roots (1,j) for j>0. The M-action on V^{natural} induces an M-action on the set of gl_2 subalgebras corresponding to a fixed imaginary simple root. I will discuss this action and related open questions. (This talk is based on joint work with Lisa Carbone, Elizabeth Jurisich, Maryam Khaqan, and Scott H. Murray).
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