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BEGIN:VEVENT
UID:61b33e169ed2fb992f7de0a953948366
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20210208T123557
SUMMARY:Positivity  of  interpolation  polynomials
LOCATION:zoom
DESCRIPTION:Abstract: The interpolation polynomials are a  family of \n inhomogeneous s
 ymmetric polynomials characterized \n by simple vanishing properties. In 19
 96, Knop and Sahi \n showed that their top homogeneous components are \n Ja
 ck polynomials. For this reason these polynomials are \n sometimes called i
 nterpolation Jack polynomials, shifted \n Jack polynomials, or Knop-Sahi po
 lynomials.\n \n We prove Knop and Sahi's main conjecture from 1996, \n whic
 h asserts that, after a suitable normalization, the \n interpolation polyno
 mials have positive integral coefficients. \n This result generalizes Macdo
 nald's conjecture for Jack \n polynomials that was proved by Knop and Sahi 
 in 1997. \n Moreover, we give a combinatorial expansion for the \n interpol
 ation polynomials that exhibits the desired \n positivity property.\n \n Th
 is is joint work with Y. Naqvi and S. Sahi.  \n
X-ALT-DESC;FMTTYPE=text/html:<p><span><span style="font-family: 'Times New Roman',serif; font-size: 12pt
 ; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso
 -fareast-language: EN-US; mso-bidi-language: AR-SA;">Abstract: The interpol
 ation polynomials are a&nbsp; family of </span></span><span style="font-fam
 ily: 'Times New Roman',serif; font-size: 12pt; mso-fareast-font-family: 'Ti
 mes New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-
 bidi-language: AR-SA;"><br /> <span>inhomogeneous symmetric polynomials cha
 racterized </span><br /> <span>by simple vanishing properties. In 1996, Kno
 p and Sahi </span><br /> <span>showed that their top homogeneous components
  are </span><br /> <span>Jack polynomials. For this reason these polynomial
 s are </span><br /> <span>sometimes called interpolation Jack polynomials, 
 shifted </span><br /> <span>Jack polynomials, or Knop-Sahi polynomials.</sp
 an><br /> <br /> <span>We prove Knop and Sahi's main conjecture from 1996, 
 </span><br /> <span>which asserts that, after a suitable normalization, the
  </span><br /> <span>interpolation polynomials have positive integral coeff
 icients. </span><br /> <span>This result generalizes Macdonald's conjecture
  for Jack </span><br /> <span>polynomials that was proved by Knop and Sahi 
 in 1997. </span><br /> <span>Moreover, we give a combinatorial expansion fo
 r the </span><br /> <span>interpolation polynomials that exhibits the desir
 ed </span><br /> <span>positivity property.</span><br /> <br /> <span>This 
 is joint work with Y. Naqvi and S. Sahi.</span><br style="mso-special-chara
 cter: line-break;" /> <br style="mso-special-character: line-break;" /> </s
 pan></p>
CONTACT:Emily Sergel, Rutgers University
X-EXTRAINFO:Zoom link: https://rutgers.zoom.us/j/93921465287\nMeeting ID: 939 2146 5287
 \nPasscode: 196884
DTSTAMP:20260829T055222
DTSTART;TZID=America/New_York:20210212T120000
DTEND;TZID=America/New_York:20210212T130000
SEQUENCE:0
TRANSP:OPAQUE
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