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SUMMARY:Finding bases of new infinite dimensional representations of $\mathfrak{osp}(1|2n)$ ( Dwight Williams\, UT Arlington)
DESCRIPTION:The orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2n)$ is rich in representation theory: while the finite dimensional $\mathfrak{osp}(1|2n)$-module category is semisimple\, the study of infinite dimensional representations of $\mathfrak{osp}(1|2n)$ is wide open. In this talk\, we will define the orthosymplectic Lie superalgebras\, realize $\mathfrak{osp}(1|2n)$ as differential operators on complex polynomials\, and describe the space of polynomials in commuting and anti-commuting variables as a representation space for $\mathfrak{osp}(1|2n)$. Moreover\, we will present operators—and perhaps generalized versions of these operators—which help give explicit bases for certain infinite dimensional $\mathfrak{osp}(1|2n)$-modules.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-dwight-williams-ut-arlington/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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