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SUMMARY:Rose Berry (UEA)
DTSTART:20250512T130000Z
DTEND:20250512T140000Z
DTSTAMP:20260421T154019Z
UID:UEAPS/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/54/">T
 he Derived l-modular Unipotent Block of p-adic GLn</a>\nby Rose Berry (UEA
 ) as part of ANTLR seminar\n\nLecture held in LT3.\n\nAbstract\nComplex re
 presentations of p-adic groups are in many ways well-understood. The categ
 ory has Bernstein's decomposition into blocks\, and for many groups each b
 lock is known to be equivalent to modules over a Hecke Algebra. In particu
 lar\, the unipotent block (the block containing the trivial representation
 ) of GLn is equivalent to the modules over an extended affine hecke algebr
 a of type A. Over \\bar{Fl} the situation is more complicated in the gener
 al case: the Bernstein block decomposition can fail (eg for SP8)\, and the
 re is no longer in general an equivalence with the Hecke algebra. However\
 , some groups\, such as GLn and its inner forms\, still have a Bernstein d
 ecomposition. Furthermore\, Vigernas showed that the unipotent block of GL
 n contains a subcategory that is equivalent to modules over a mild extensi
 on of the Hecke Algebra\, the Schur Algebra\, and this subcategory generat
 es the principal block under extensions. Building on this work\, we show t
 hat the derived category of the principal block of GLn is triangulated-equ
 ivalent to the perfect complexes over a dg-enriched Schur algebra. We prov
 e this by combining general finiteness results about Schur algebras with t
 he well-known structure of the l-modular unipotent blocks of GLn over fini
 te fields.\n
LOCATION:https://researchseminars.org/talk/UEAPS/54/
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