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2023年6月27日(火) 15:00~16:30
i-Siteなんば S1での対面およびZoomのハイブリッド形式
Oscillator representations of quantum affine orthosymplectic superalgebras
We introduce a category of q-oscillator representations over the quantum affine superalgebras of type D and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these irreducible representations naturally interpolate the irreducible q-oscillator representations of type ${X}^{(1)} _n$ and the finite-dimensional irreducible representations of type ${Y}^{(1)} _n$ for $(X,Y)=(C,D),(D,C)$ under exact monoidal functors. This can be viewed as a quantum (untwisted) affine analogue of the correspondence between irreducible oscillator and irreducible finite-dimensional representations of classical Lie algebras arising from the Howe’s reductive dual pairs $(g,G)$, where $g=sp _{2n},so _{2n}$ and $G=O _l,Sp _{2l}$. This talk is based on arXiv:2304.06215, which is a joint work with Jae-Hoon Kwon and Sin-Myung Lee.