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UID:2033c49e0432151c58376281d4c18ad0
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20221028T101747
SUMMARY:Vertex operators for imaginary gl_2-subalgebras in the Monster Lie Algebra
LOCATION:Zoom
DESCRIPTION:Abstract The Monster Lie algebra m is a quotient of the physical space of t
 he vertex algebra V=V^<br/>aturalotimes V_{1,1}, where V^<br/>atural is the
  Moonshine module of Frenkel, Lepowsky, and Meurman, and V_{1,1} is the ver
 tex 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 $mathbb{M}$ ac
 ts 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 th
 e Serre-Chevalley generators of families of gl_2-subalgebras corresponding 
 to the imaginary simple roots (1,n) of m for 0<n<100. We prove the existenc
 e of primary vectors in V^<br/>atural of each homogeneous weight $n$ and, f
 or $0<n<100$, we show that there exist primary vectors that can be used to 
 construct the elements in $V$ corresponding to the generators of our gl_2-s
 ubalgebras.  We show that the action of M on V^<br/>atural induces an actio
 n on the Serre-Chevalley generators of the aforementioned subalgebras. We c
 onjecture  that this M-action is non-trivial.This talk is based on joint wo
 rk with Lisa Carbone, Elizabeth Jurisich, Maryam Khaqan, and Scott H. Murra
 y. 
CONTACT:Speaker Darlayne Addabbo, University of Arizona 
X-EXTRAINFO:Zoom link https://rutgers.zoom.us/j/93921465287\nMeeting ID: 939 2146 5287\
 nPasscode: 196884, the dimension of the weight 2 homogeneous \nsubspace of 
 the moonshine module
DTSTAMP:20260907T040917
DTSTART;TZID=America/New_York:20221111T121000
DTEND;TZID=America/New_York:20221111T131000
SEQUENCE:0
TRANSP:OPAQUE
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