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UID:71e294b5fca3bcf1ad154e0d59bda35e
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20241119T223240
SUMMARY:Basic orthogonal polynomials of Jacobi type 
LOCATION:Hill 705
DESCRIPTION:<p>Many important classical families of orthogonal polynomials, such as Jac
 obi, Laguerre, Legendre, etc., arise via specialization from some hypergeom
 etric series or from a q-analog (the so-called basic series). The Askey sch
 eme is a hierarchical list of some 48 such families, and it is natural to a
 sk if this list is complete.</p><p>In joint work with Joseph Bernstein and 
 Dmitry Gourevitch (<a href="https://arxiv.org/abs/2401.14715"></a><a href="
 https://arxiv.org/abs/2401.14715">https://arxiv.org/abs/2401.14715</a>), we
  have axiomatized some part of the Askey scheme, which we refer to as famil
 ies of Jacobi type, and discovered 2 new families.</p><p>In this lecture I 
 will describe the q-analog of the above result, namely the definition and c
 lassification of polynomials of basic Jacobi type. It turns out that in thi
 s setting there are 4 new families beyond the Askey scheme.</p><p>We are in
  the process of extending our results to obtain a complete classification o
 f hypergeometric and basic orthogonal polynomials. Our expectation is that 
 we will recover the full Askey scheme along with a small number of new fami
 lies.</p>
CONTACT:Siddhartha Sahi, Rutgers University 
DTSTAMP:20260827T020844
DTSTART;TZID=America/New_York:20241122T121000
DTEND;TZID=America/New_York:20241122T131000
SEQUENCE:0
TRANSP:OPAQUE
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