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SUMMARY:Santosh Nadimpalli (IIT Kanpur)
DTSTART:20220217T060000Z
DTEND:20220217T070000Z
DTSTAMP:20260423T024448Z
UID:ARCSIN/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ARCSIN/14/">
 On uniqueness of branching to fixed point Lie subalgebras</a>\nby Santosh 
 Nadimpalli (IIT Kanpur) as part of ARCSIN - Algebra\, Representations\, Co
 mbinatorics and Symmetric functions in INdia\n\n\nAbstract\nLet $\\mathfra
 k{g}$ be a complex semisimple Lie algebra and let\n  $\\theta$ be a finite
  order automorphism of $\\mathfrak{g}$. We assume\n  that any ${\\rm A}_{2
 n}$-type $\\theta$-stable indecomposable ideal of\n  $\\mathfrak{g}$ is si
 mple and any ${\\rm D}_k$\, ${\\rm A}_{2k+1}$ and\n  ${\\rm E}_6$-type $\\
 theta$-stable indecomposable ideal of\n  $\\mathfrak{g}$ has length at mos
 t $2$. Let $\\mathfrak{g}_0$ be the\n  fixed point subalgebra of $\\mathfr
 ak{g}$.  In this talk\, for any\n  irreducible finite dimensional represen
 tations $V_1$ and $V_2$ of\n  $\\mathfrak{g}$\, we show that\n${\\rm res}_
 {\\mathfrak{g}_0}V_1\\simeq \n{\\rm res}_{\\mathfrak{g}_0}V_2$ if and only
  if $V_2$ is isomorphic to\n$V_1^\\sigma$\, for some outer automorphism $\
 \sigma$ of $\\mathfrak{g}$.\n
LOCATION:https://researchseminars.org/talk/ARCSIN/14/
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