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SUMMARY:Sridhar P Naryanan (The Institute of Mathematical Sciences\, Chenn
 ai)
DTSTART:20210319T093000Z
DTEND:20210319T103000Z
DTSTAMP:20260423T021530Z
UID:ARCSIN/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ARCSIN/2/">M
 ultiplicity of trivial and sign representations of $S_n$ in hook-shaped re
 presentations of $GL_n$.</a>\nby Sridhar P Naryanan (The Institute of Math
 ematical Sciences\, Chennai) as part of ARCSIN - Algebra\, Representations
 \, Combinatorics and Symmetric functions in INdia\n\n\nAbstract\nLet $W_\\
 lambda$ be an irreducible representation of $GL_n$ (for\npartition $\\lamb
 da$ with $\\leq n$ parts). Let $V_\\mu$ be an irreducible\nrepresentation 
 of $S_n$ (for partition $\\mu \\vdash n$). Then $$W_\\lambda=\n\\sum_{\\mu
  \\vdash n} r_{\\lambda \\mu} V_\\mu.$$\nThe coefficients $r_{\\lambda\\mu
 }$ are the restriction coefficients. The\nrestriction problem is to find c
 ombinatorial objects that these coefficients\ncount. We find such objects 
 when $\\lambda$ is the hook shape and $\\mu=(n)$\nor $\\mu= (1^n)$ using t
 he theory of character polynomials and a simple\nsign-reversing involution
 .\n
LOCATION:https://researchseminars.org/talk/ARCSIN/2/
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