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SUMMARY:Sabino di Trani (University of Florence)
DTSTART:20210114T130000Z
DTEND:20210114T140000Z
DTSTAMP:20260423T024652Z
UID:AlBicocca/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AlBicocca/9/
 ">Combinatorics of Exterior Algebra\, Graded Multiplicities and Generalize
 d Exponents of Small Representations</a>\nby Sabino di Trani (University o
 f Florence) as part of Al@Bicocca take-away\n\n\nAbstract\nLet $\\mathfrak
 {g}$ be a simple Lie algebra over $\\mathbb{C}$\, and consider the exterio
 r algebra $\\wedge\\mathfrak{g}$ as $\\mathfrak{g}$-representations. In th
 e talk we will give an overview of some conjectures and of many elegant re
 sults proved in the past century about the irreducible decomposition of $\
 \wedge\\mathfrak{g}$. We will focus on a Conjecture due by Reeder that gen
 eralizes the classical result about invariants in $\\wedge\\mathfrak{g}$ t
 o a special class of representations\, called "small". Reeder conjectured 
 that it is possible to compute the graded multiplicities in $\\wedge\\math
 frak{g}$ of this special class of representations reducing to a "Weyl grou
 p representation" problem. We will give an idea of the strategy we used to
  prove the conjecture in the classical case\, introducing the most relevan
 t instruments we used and we will outline the difficulties we faced with. 
 Finally\, we will expose how our formulae can be rearranged involving the 
 Generalized Exponents of small representations\, obtaining a generalizatio
 n of some classical formulae for graded multiplicities in the adjoint and 
 little adjoint case.\n
LOCATION:https://researchseminars.org/talk/AlBicocca/9/
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