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Let $G = \mathrm{GL}_n(F)$ where $F$ = non-archimedean local field. The Langlands Classification tells one that all irreducible admissible reps of $\mathrm{GL}_n(F)$ can be realized as (the unique irreducible) quotient of a parabolicly induced representation.
In particular, if one takes a (multip...
In mathematics, the Steinberg representation, or Steinberg module or Steinberg character, denoted by St, is a particular linear representation of a reductive algebraic group over a finite field or local field, or a group with a BN-pair. It is analogous to the 1-dimensional sign representation ε of a Coxeter or Weyl group that takes all reflections to –1.
For groups over finite fields, these representations were introduced by Robert Steinberg (1951, 1956, 1957), first for the general linear groups, then for classical groups, and then for all Chevalley groups, with a construction that immediately...
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Q: Has anyone seen this construction of the Weil representation of $\mathrm{Sp}_{2k}(\mathbb{F}_p)$?
$\def\FF{\mathbb{F}}\def\CC{\mathbb{C}}\def\QQ{\mathbb{Q}}\def\Sp{\text{Sp}}\def\SL{\text{SL}}\def\GL{\text{GL}}\def\PGL{\text{PGL}}$Let $p$ be an odd prime. The Weil representation is a $p^k$-dimensional complex representation of $\Sp_{2k}(\FF_p)$. If you read most descriptions of the Weil repre...
In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the ring of adeles.
The metaplectic group has a particularly significant infinite-dimensional linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and is important in the theory of modular forms of half-integral weight and the theta correspondence.
== Definition ==
The...
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I am searching for an interesting masters thesis topic connecting mathematics and mechanical engineering.
Perhaps statistics and mechanical engineering. Any good ideas?
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Note: My first question in this site. MSE users asked me to post this question here for better response
I am a Masters student in Pure Mathematics.
I need to do a Masters thesis in "Linear Algebra in Graph Theory" where I will have to publish some original work in our Departmental Journal mean...
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I search for a big list of open problems which have been solved in a PhD thesis by the Author of the thesis (or with collaboration of her/his supervisor).
In my question I search for every possible open problem but I prefer (but not limited) to receive answers about those open problems which ha...
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It seems that there is no digital copy of Leon Karp's Ph.D. thesis
L. Karp, Vector fields on manifolds, Thesis, New York Univ., 1976.
on internet and his paper excerpted from his thesis is very brief and without any detailed proof. (I wonder that peers read the thesis or they trust to the advisor...
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