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SUMMARY:Adèle Bourgeois
DTSTART:20200529T160000Z
DTEND:20200529T162000Z
DTSTAMP:20260417T131011Z
UID:CARTOON/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CARTOON/5/">
 Restricting representations via restricting $G$-data and Kim-Yu types</a>\
 nby Adèle Bourgeois as part of Cross Atlantic Representation Theory and O
 ther topics ONline (CARTOON) conference\n\n\nAbstract\nLet $\\mathbb{G}$ b
 e a reductive group defined over a $p$-adic field $F$\, and let $G = \\mat
 hbb{G}(F)$. We assume that $\\mathbb{G}$ splits over a tamely ramified ext
 ension of $F$ and that the residual characteristic $p$ of $F$ does not div
 ide the order of the Weyl group of $\\mathbb{G}$. Under this assumption\, 
 Fintzen showed that all irreducible supercuspidal representations of $G$ a
 re obtained via the J.K.~Yu construction. From a $G$-datum $\\Psi$\, the J
 .K.~Yu construction produces an irreducible supercuspidal representation o
 f $G$\, which we denote by $\\pi_G(\\Psi)$. \n\nGiven a reductive $F$-subg
 roup $\\mathbb{H}$ that contains the derived subgroup of $\\mathbb{G}$\, w
 e study the restriction $\\pi_G(\\Psi)|_H$ and obtain a description of its
  decomposition into irreducible components along with their multiplicities
 . We achieve this by describing a natural restriction process from which w
 e construct $H$-data from the $G$-datum $\\Psi$. \n\nTo study the restrict
 ion to $H$ of irreducible representations of $G$ which are not supercuspid
 al\, one can use the theory of types. More specifically\, given the underl
 ying assumption on $p$\, Fintzen showed that every irreducible representat
 ion of $G$ contains a Kim-Yu type. The construction of Kim-Yu types is ver
 y similar to Yu's construction of supercuspidal representations. As such\,
  we can define an analogous restriction process from which we construct Ki
 m-Yu types for $H$ from a Kim-Yu type for $G$\, therefore obtaining inform
 ation on the restriction to $H$ of any irreducible representation of $G$.\
 n
LOCATION:https://researchseminars.org/talk/CARTOON/5/
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