# Seminars & Colloquia Calendar

Lie Group Quantum Mathematics Seminar

## Vertex operators for imaginary gl_2-subalgebras in the Monster Lie Algebra

#### Speaker Darlayne Addabbo, University of Arizona

Location:  Zoom
Date & time: Friday, 11 November 2022 at 12:10PM - 1:10PM

Abstract The Monster Lie algebra m is a quotient of the physical space of the vertex algebra V=V^
aturalotimes V_{1,1}, where V^
atural is the Moonshine module of Frenkel, Lepowsky, and Meurman, and V_{1,1} is the vertex algebra corresponding to the rank 2 even unimodular lattice II_{1,1}. It is known that $$mathfrak m$$ has gl_2-subalgebras generated by both real and imaginary root vectors and that the Monster simple group $$mathbb{M}$$ acts trivially on the gl_2-subalgebra corresponding to the unique real simple root. We construct elements of V that project under the quotient map to the Serre-Chevalley generators of families of gl_2-subalgebras corresponding to the imaginary simple roots (1,n) of m for 0 atural of each homogeneous weight $n$ and, for \$0 atural induces an action on the Serre-Chevalley generators of the aforementioned subalgebras. We conjecture that this M-action is non-trivial. This talk is based on joint work with Lisa Carbone, Elizabeth Jurisich, Maryam Khaqan, and Scott H. Murray.