labirintas
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Unregistered User
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Jan 28 |
awarded | ● Commentator |
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Jan 28 |
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Explicit Casselman theory: reference needed A similar question has been asked: mathoverflow.net/questions/115933/… |
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Dec 17 |
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Serre functor of an injective module He wants to derive the functor of global sections in the category of sheaves of abelian groups, and not in the category of quasi-coherent sheaves. His argument shows that the two notions coincide. Let me give you an example, where they don't: Let $G$ be a $p$-group, let $R$ be the category of all $\mathbb{F}_p$-representations of $G$ and let $V$ be the full subcategory of $R$, consisting of vector spaces with trivial $G$ -action. If you derive the functor $r\mapsto r^G$ (the invariants), then the derived functors in $V$ are zero, and non-zero in $R$. |
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Dec 10 |
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How to think about parabolic induction. I guess the argument for p-adic groups is also an induction-restriction argument, which OP doesn't like. |
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Dec 10 |
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What is the support of the Whittaker function of a new vector on GL(2)? Why is W non-zero on the centre? All you know that W is non-zero on some coset $U g K_1(c)Z$. Paskunas-Stevens compute some Whittaker functions for supercuspidals, see arxiv.org/abs/math/0603051, but the fucntions there will not be new vectors in general, i think. |
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Dec 10 |
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How to think about parabolic induction. In the previous comment I consider representations of $GL_2(F_p)$ on $F_p$-vector spaces. |
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Dec 10 |
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How to think about parabolic induction. Let me just note that this fails if you consider modular representations. So if you induce a regular character $\chi$ from the upper triangular matrices in $GL_2(F_p)$ and from the lower triangular matrices, you get non-isomorphic representations, which have the same semi simplification. Regular means $\chi^s\neq \chi$, and $s$ is the matrix (0 & 1// 1 & 0). |
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Dec 3 |
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Prime divisor of finite group What do you sum over in the last sum? Over all the conjugacy classes? |
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Dec 3 |
answered | Matrices over Finite Prime Fields |
