Reputation
772
Next privilege 1,000 Rep.
See votes, expandable usercard
Badges
8 27
Impact
~52k people reached

Apr
5
awarded  Notable Question
Sep
18
comment Well-understood bases for Grothendieck groups of modular representation categories
Okay. I was thinking about Weyl modules for the restricted Lie algebra (given by choosing an integral form of the representation in characteristic 0), and reducing the coefficients modulo p. The module category in question is also for the restricted Lie algebra (ie. zero p-character), with a fixed singular, generalized HC character (these appear, for instance, in [BMR] localization theory). Thanks. [I understand one loses a lot of information by decategorifying; but I'm trying to show that a certain identity holds there, so that's all I need.]
Sep
17
comment Well-understood bases for Grothendieck groups of modular representation categories
Thanks, I've had a look. One last question: so the block I'm interested in (with $0$ p-character, and singular HC character) contains infinitely many Weyl modules. Do the classes of these modules span the Grothendieck group? I think this should be true, since two modules with different characters have different images in $K^0$ (and one can compute the characters of these modules).
Sep
16
accepted Well-understood bases for Grothendieck groups of modular representation categories
Sep
15
comment Well-understood bases for Grothendieck groups of modular representation categories
Okay - do you mean your notes in the AMS Bulletins? Are there are Weyl modules which lie in the category where the Frobenius character $\chi = 0$, and the Harish-Chandra character is singular (perhaps $\Gamma(O(\lambda))$, where $\lambda$ is a singular weight)? I don't need them to play the role of highest weight modules; all I want is a spanning set in $K^0$. Thanks.
Sep
14
comment Well-understood bases for Grothendieck groups of modular representation categories
Thanks for the response. I think the linear function $\chi$ that you refer to is the character of the Frobenius center that I mentioned. I don't necessarily need a "natural" basis - a collection of objects which span the Grothendieck group would be good enough for me. What if one applies translation functors to Weyl modules (so that they land inside the singular categories) -- would that be useful?
Sep
14
asked Well-understood bases for Grothendieck groups of modular representation categories
Sep
9
awarded  Popular Question
Jun
1
awarded  Notable Question
Sep
28
awarded  Popular Question
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
Jun
26
accepted Pushforwards/pullbacks of some line bundles on (partial) flag varieties
Jun
26
revised Computing tangent spaces of resolutions to Slodowy slices
added 69 characters in body
Jun
25
asked Computing tangent spaces of resolutions to Slodowy slices
May
28
revised The prime numbers modulo $k$, are not periodic
Improved notation.
May
28
suggested approved edit on The prime numbers modulo $k$, are not periodic
May
25
accepted Explicit computations of small Deligne-Lusztig varieties (e.g. Drinfeld curve)
May
11
revised Decomposing tensor products of irreducible representations of reductive groups over a finite field
deleted 516 characters in body
Mar
3
awarded  Popular Question