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SUMMARY:Amritanshu Prasad (IMSc\, Chennai)
DTSTART:20200827T103000Z
DTEND:20200827T113000Z
DTSTAMP:20260423T022922Z
UID:SF-and-nt/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SF-and-nt/6/
 ">Character Polynomials and their Moments</a>\nby Amritanshu Prasad (IMSc\
 , Chennai) as part of Special Functions and Number Theory seminar\n\n\nAbs
 tract\nA polynomial in a sequence of variables can be regarded as a class 
 \nfunction on every symmetric group when the $i$th variable is interpreted
  as \nthe number of $i$-cycles. Many nice families of representations of s
 ymmetric \ngroups have characters represented by such polynomials.\n\nWe i
 ntroduce two families linear functionals of this space of polynomials -- m
 oments and signed moments. For each $n$\, the moment of a polynomial at $n
 $ \ngives the average value of the corresponding class function on the $n$
 th \nsymmetric group\, while the signed moment gives the average of its \n
 product by the sign character. These linear functionals are easy to \ncomp
 ute in terms of binomial bases of the space of polynomials.\n\nWe use them
  to explore some questions in the representation theory of \nsymmetric gro
 ups and general linear groups. These explorations lead to \ninteresting ex
 pressions involving multipartite partition functions and \nsome peculiar v
 ariants.\n
LOCATION:https://researchseminars.org/talk/SF-and-nt/6/
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