BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:An affine Weyl group action on the basic hypergeometric series ari
 sing from the $q$-Garnier system
DTSTART;VALUE=DATE-TIME:20230619T150000Z
DTEND;VALUE=DATE-TIME:20230619T153000Z
DTSTAMP;VALUE=DATE-TIME:20260916T204425Z
UID:indico-contribution-14@cern.ch
DESCRIPTION:Speakers: Prof. SUZUKI\, Takao (Kindai University)\nThe Garnie
 r system is an extension of the sixth Painlev\\'e equation from a viewpoin
 t of the isomonodromy deformation of a Fuchsian system.\nIts $q$-differenc
 e analogue was proposed by Sakai as the connection preserving deformation 
 of a linear $q$-difference system.\nRecently\, we formulated the $q$-Garni
 er system in a framework of an extended affine Weyl group of type $A^{(1)}
 _{2n+1}\\times A^{(1)}_1\\times A^{(1)}_1$.\nOn the other hand\, the $q$-G
 arnier system admits a particular solution in terms of the basic hypergeom
 etric series ${}_{n+1}\\phi_n$.\nThen it becomes the next problem to inves
 tigate an action of the extended affine Weyl group on ${}_{n+1}\\phi_n$.\n
 In this talk\, we give an answer to this problem.\nNamely\, we give a left
  action of a subgroup of the extended affine Weyl group on a vector whose 
 components are described in terms of ${}_{n+1}\\phi_n$.\nHence $q$-contigu
 ity relations and a linear $q$-difference equation for ${}_{n+1}\\phi_n$ c
 an be derived from the extended affine Weyl group systematically.\n\nhttp:
 //indico.fuw.edu.pl/contributionDisplay.py?contribId=14&sessionId=16&confI
 d=67
LOCATION:Faculty of Physics\, University of Warsaw Lecture hall: 0.06
URL:http://indico.fuw.edu.pl/contributionDisplay.py?contribId=14&sessionId
 =16&confId=67
END:VEVENT
END:VCALENDAR