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SUMMARY:Ana Kontrec (RIMS\, Kyoto University)
DTSTART:20230227T150000Z
DTEND:20230227T160000Z
DTSTAMP:20260423T021108Z
UID:EQuAL/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EQuAL/8/">Re
 presentation theory and duality properties of some affine W-algebras</a>\n
 by Ana Kontrec (RIMS\, Kyoto University) as part of European Quantum Algeb
 ra Lectures (EQuAL)\n\n\nAbstract\nOne of the most important families of v
 ertex algebras are affine vertex algebras and their associated $\\mathcal{
 W}$-algebras\, which are connected to various aspects of geometry and phys
 ics. Among the simplest examples of $\\mathcal{W}$-algebras is the Bershad
 sky-Polyakov vertex algebra $\\mathcal{W}^k(\\mathfrak{g}\, f_{min})$\, as
 sociated to $\\mathfrak{g} = sl(3)$  and the minimal nilpotent element $f_
 {min}$.\nIn this talk we are particularly interested in the Bershadsky-Pol
 yakov algebra $\\mathcal W_k$  at positive integer levels\, for which we o
 btain a complete classification of irreducible modules.\nIn the case  $k=1
 $\, we show that this vertex algebra has a Kazama-Suzuki-type dual isomorp
 hic to the simple affine vertex superalgebra $L_{k'} (osp(1 \\vert 2))$ fo
 r $k'=-5/4$. This is joint work with D. Adamovic.\n
LOCATION:https://researchseminars.org/talk/EQuAL/8/
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