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SUMMARY:Chun-Ju Lai (Academia Sinica)
DTSTART:20221025T003000Z
DTEND:20221025T013000Z
DTSTAMP:20260423T021250Z
UID:OISTRTS/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/41/"
 >Quasi-hereditary covers\, Hecke subalgebras and quantum wreath product</a
 >\nby Chun-Ju Lai (Academia Sinica) as part of OIST representation theory 
 seminar\n\n\nAbstract\nThe Hecke algebra is in general not quasi-hereditar
 y\, meaning that its module category is not a highest weight category\; wh
 ile it admits a quasi-hereditary cover via category O for certain rational
  Cherednik algebras due to Ginzburg-Guay-Opdam-Rouquier. It was proved in 
 type A that this category O can be realized using q-Schur algebra\, but th
 is realization problem remains open beyond types A/B/C. An essential step 
 for type D is to study Hu's Hecke subalgebra\, which deforms from a wreath
  product that is not a Coxeter group. In this talk\, I'll talk about a new
  theory allowing us to take the ``quantum wreath product'' of an algebra b
 y a Hecke algebra. Our wreath product produces the Ariki-Koike algebra as 
 a special case\, as well as new ``Hecke algebras'' of wreath products betw
 een symmetric groups. We expect them to play a role in answering the reali
 zation problem for complex reflection groups. This is a joint work with Da
 n Nakano and Ziqing Xiang.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/41/
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