34,573 research outputs found
Remarks on the symmetric powers of cusp forms on GL(2)
In this paper we prove the following conditional result: Let F be a number
field, and pi a cusp form on GL(2)/F which is not solvable polyhedral. Assume
that all the symmetric powers sym^m(pi) are modular, i.e., define automorphic
forms on GL(m+1)/F. If sym^6(pi) is cuspidal, then all the symmetric powers are
cuspidal, for all m. Moreover, sym^6(pi) is Eisenteinian iff sym^5(pi) is an
abelian twist of the functorial product of pi with the symmetric square of a
cusp form pi' on GL(2)/F.Comment: A sentence has been modified in the Introduction. It has nothing to
do with the main result of the pape
Modular generalized Springer correspondence: an overview
This is an overview of our series of papers on the modular generalized
Springer correspondence. It is an expansion of a lecture given by the second
author in the Fifth Conference of the Tsinghua Sanya International Mathematics
Forum, Sanya, December 2014, as part of the Master Lecture `Algebraic Groups
and their Representations' Workshop honouring G. Lusztig. The material that has
not appeared in print before includes some discussion of the motivating idea of
modular character sheaves, and heuristic remarks about geometric functors of
parabolic induction and restriction.Comment: 19 pages. Version 2 includes more examples and tables in Section
On the weights of mod Hilbert modular forms
We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the
possible weights of mod Hilbert modular forms, by making use of modularity
lifting theorems and computations in -adic Hodge theory.Comment: 34 pages. Essentially final version, to appear in Inventiones
mathematicae. This version does not incorporate any minor changes (e.g.
typographical changes) made in proo
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