BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:Lie Groups Seminar
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20261012T001753Z
UID:tag:localist.com\,2008:EventInstance_52444732757655
DTSTART:20260415T190000Z
DTEND:20260415T203000Z
DESCRIPTION:👉Special time and location:  3 PM in 5-234👈\n\nSpeaker: X
 uhua He (University of Hong Kong)\n\nTitle: Positivity of Canonical Bases\
 n\nAbstract: Lusztig's theory of canonical bases reveals a remarkably rigi
 d and positive algebraic structure on quantum groups and their modules. In
  symmetric types\, it is known that the structure constants for multiplica
 tion in the negative part U−\, as well as for the action of Chevalley ge
 nerators Ei and Fi on a single simple module\, all belong to ℕ [v\,v-1].
 \n\n \n\nLusztig conjectured that this strong positivity holds for the mul
 tiplication within the modified quantum group and the action on the tensor
  product of modules. In this talk\, I will present recent joint work with 
 Jiepeng Fang towards this conjecture.\n\n \n\nA key innovation in our appr
 oach is the "thickening philosophy"\, an algebraic technique inspired by g
 eometric ideas from total positivity\, motivated on my earlier work with H
 uanchen Bao. This method embeds a suitable approximation of the tensor pro
 duct into the negative part Ũ− of a larger quantum group\, constructed
  via a framed quiver. This allows us to inherit the desired positivity dir
 ectly from the well-established positivity of the canonical basis of Ũ
 −. This approach demonstrates how the large Kac-Moody groups can provide
  a powerful framework for elucidating the structure and representations of
  quantum groups even for the finite and affine types.
GEO:42.358883;-71.093478
LOCATION:Building 5\, 234
SUMMARY:Lie Groups Seminar
URL;VALUE=URI:https://calendar.mit.edu/event/lie-groups-seminar-2659
CATEGORIES:Conferences/Seminars/Lectures
END:VEVENT
END:VCALENDAR