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UID:991e95bf7f4de6414cbf30d79218db92
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20221121T114259
SUMMARY:Determinantal inequalities for totally positive matrices
LOCATION:Hill Center Room 705
DESCRIPTION:<p><strong>Abstract </strong>Totally positive matrices are matrices in whic
 h each minor is positive. <br> Lusztig extended the notion to reductive Lie
  groups. He also proved that <br> specialization of elements of the dual ca
 nonical basis in representation <br> theory of quantum groups at q=1 are to
 tally non-negative polynomials. <br> Thus, it is important to investigate c
 lasses of functions on matrices that <br> are positive on totally positive 
 matrices. I will discuss two sourses of <br> such functions. One has to do 
 with multiplicative determinantal inequalities <br> (joint work with M. Gek
 htman). Another deals with majorizing monotonicity <br> of symmetrized Fisc
 her's products which are known for hermitian positive <br> semidefinite cas
 e which brings additional motivation to verify if they hold <br> for totall
 y positive matrices as well (joint work with M. Skandera). The main <br> to
 ols we employed are network parametrization, Temperley-Lieb and <br> monomi
 al trace immanants.</p><p>The information has also been posted in our semin
 ar web page:<br> <a href="https://sites.math.rutgers.edu/~yzhuang/rci/math/
 lie-quantum.html" moz-do-not-send="true"></a><a href="https://sites.math.ru
 tgers.edu/~yzhuang/rci/math/lie-quantum.html">https://sites.math.rutgers.ed
 u/~yzhuang/rci/math/lie-quantum.html</a></p>
CONTACT:Daniel Soskin, University of Notre Dame
DTSTAMP:20260922T051704
DTSTART;TZID=America/New_York:20221202T121000
DTEND;TZID=America/New_York:20221202T131000
SEQUENCE:0
TRANSP:OPAQUE
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