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UID:6835d50f33a2da303fc4d51fe613c545
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20210315T104344
SUMMARY:Combinatorial formula for SSV polynomials 
LOCATION:Zoom
DESCRIPTION:<p><strong>Abstract </strong>Macdonald polynomials are homogeneous polynomi
 als that generalize many important representation-theoretic families of pol
 ynomials, such as Jack polynomials, Hall-Littlewood polynomials, affine Dem
 azure characters, and Whittaker functions of GL_r(F) (where F is a non-Arch
 imedean field). They may be constructed using the basic representation of t
 he corresponding double affine Hecke algebra (DAHA): a particular commutati
 ve subalgebra of the DAHA acts semisimply on the space of polynomials, and 
 the (nonsymmetric) Macdonald polynomials are the simultaneous eigenfunction
 s. In 2018, Sahi, Stokman, and Venkateswaran constructed a generalization o
 f this DAHA action, recovering the metaplectic Weyl group action of Chinta 
 and Gunnells. As a consequence, they discovered a new family of polynomials
 , called SSV polynomials, that generalize both Macdonald polynomials and Wh
 ittaker functions of metaplectic covers of GL_r(F). We will give a combinat
 orial formula for these SSV polynomials in terms of alcove walks, generaliz
 ing Ram and Yip's formula for Macdonald polynomials.</p>
CONTACT:Jason Saied, Rutgers University  
X-EXTRAINFO:Zoom link https://rutgers.zoom.us/j/93921465287\nMeeting ID: 939 2146 5287\
 nPasscode: 196884
DTSTAMP:20260830T052114
DTSTART;TZID=America/New_York:20210326T120000
DTEND;TZID=America/New_York:20210326T130000
SEQUENCE:0
TRANSP:OPAQUE
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