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SUMMARY:Jonah Blasiak (Drexel University)
DTSTART:20210419T190000Z
DTEND:20210419T200000Z
DTSTAMP:20260423T024546Z
UID:YUAAS/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/YUAAS/31/">A
  raising operator formula for $\\nabla$ on an LLT polynomial</a>\nby Jonah
  Blasiak (Drexel University) as part of York University Applied Algebra Se
 minar\n\n\nAbstract\nThe symmetric function operator $\\nabla$ arose in th
 e theory of Macdonald polynomials and its action on various bases has been
  the subject of numerous conjectures over the last two decades. It develop
 ed that $\\nabla$ is but a shadow of a more complete picture involving the
  elliptic Hall algebra of Burban and Schiffmann. This algebra is generated
  by subalgebras $\\Lambda(X^{m\,n})$ isomorphic to the ring of symmetric f
 unctions\, one for each coprime pair of integers $(m\,n)$. We identify cer
 tain combinatorially defined rational functions which correspond to LLT po
 lynomials in any of the subalgebras $\\Lambda(X^{m\,n})$. As a corollary\,
  we deduce an explicit raising operator formula for $\\nabla$ on any LLT p
 olynomial.\nThis is joint work with Mark Haiman\, Jennifer Morse\,  Anna P
 un\, and George Seelinger.\n
LOCATION:https://researchseminars.org/talk/YUAAS/31/
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