BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexandra Utiralova (MIT) DTSTART:20220414T185000Z DTEND:20220414T195000Z DTSTAMP:20260423T041509Z UID:GPRTatNU/52 DESCRIPTION:Title: Harish-Chandra bimodules in complex rank\nby Alexandra Utiralova (MI T) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n\n Abstract\nThe Deligne tensor categories are defined as an interpolation of the categories of representations of groups $GL_n$\, $O_n$\, $Sp_{2n}$\, or $S_n$ to the complex values of the parameter $n$. One can extend many c lassical representation-theoretic notions and constructions to this contex t. These complex rank analogs of classical objects provide insights into t heir stable behavior patterns as n goes to infinity.\n\nI will talk about some of my results on Harish-Chandra bimodules in the Deligne cateogories. It is known that in the classical case simple Harish-Chandra bimodules ad mit a classification in terms of W-orbits of certain pairs of weights. How ever\, the notion of weight is not well-defined in the setting of the Deli gne categories. I will explain how in complex rank the above-mentioned cla ssification translates to a condition on the corresponding (left and right ) central characters.\n\nAnother interesting phenomenon arising in complex rank is that there are two ways to define harish-Chandra bimodules. That is\, one can either require that the center acts locally finitely on a bim odule $M$ or that $M$ has a finite K-type. The two conditions are known to be equivalent for a semi-simple Lie algebra in the classical setting\, ho wever in the Deligne categories\, it is no longer the case. I will talk ab out a way to construct examples of Harish-Chandra bimodules of finite K-ty pe using the ultraproduct realization of the Deligne categories.\n LOCATION:https://researchseminars.org/talk/GPRTatNU/52/ END:VEVENT END:VCALENDAR