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pro vyhledávání: '"Plymen, Roger"'
Autor:
Aubert, Anne-Marie, Plymen, Roger
We consider the depth-zero supercuspidal $L$-packets of $\mathrm{SL}_2$. With the aid of the classical character formulas of Sally-Shalika, we prove the endoscopic character identities. For the depth-zero $L$-packet of cardinality $4$, we find that,
Externí odkaz:
http://arxiv.org/abs/2410.20183
The compact, connected Lie group $E_6$ admits two forms: simply connected and adjoint type. As we previously established, the Baum-Connes isomorphism relates the two Langlands dual forms, giving a duality between the equivariant K-theory of the Weyl
Externí odkaz:
http://arxiv.org/abs/2205.08230
Autor:
Plymen, Roger
We give a streamlined account of $2$-spinors, up to and including the Dirac equation, using little more than the resources of linear algebra. We prove that the Dirac bundle is isomorphic to the associated bundles $\mathrm{SL}_2(\mathbb{C}) \times_{\m
Externí odkaz:
http://arxiv.org/abs/2204.12842
Autor:
Aubert, Anne-Marie, Plymen, Roger
Let $E/F$ be a finite and Galois extension of non-archimedean local fields. Let $G$ be a connected reductive group defined over $E$ and let $M: = \mathfrak{R}_{E/F}\, G$ be the reductive group over $F$ obtained by Weil restriction of scalars. We inve
Externí odkaz:
http://arxiv.org/abs/2007.00946
Autor:
Aubert, Anne-Marie, Plymen, Roger
Let $K$ be a non-archimedean local field. In the local Langlands correspondence for tori over $K$, we prove an asymptotic result for the depths.
Comment: 6 pages. This article supersedes arXiv:1809.10625
Comment: 6 pages. This article supersedes arXiv:1809.10625
Externí odkaz:
http://arxiv.org/abs/1810.08046
Autor:
Plymen, Roger
Let $K$ be a local field of characteristic $p$. We consider the local Langlands correspondence for tori, and construct examples for which depth is not preserved.
Comment: 3 pages; revised proof on p.2, results now more general
Comment: 3 pages; revised proof on p.2, results now more general
Externí odkaz:
http://arxiv.org/abs/1809.10625
In this paper we construct an equivariant Poincar\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended affine We
Externí odkaz:
http://arxiv.org/abs/1711.10281
Publikováno v:
Banach Centre Publications 120 (2020), 245-265
We review Morita equivalence for finite type $k$-algebras $A$ and also a weakening of Morita equivalence which we call stratified equivalence. The spectrum of $A$ is the set of equivalence classes of irreducible $A$-modules. For any finite type $k$-a
Externí odkaz:
http://arxiv.org/abs/1705.01404
Let $\mathbf{S}_k$ denote a maximal torus in the complex Lie group $\mathbf{G} = \mathrm{SL}_n(\mathbb{C})/C_k$ and let $T_k$ denote a maximal torus in its compact real form $\mathrm{SU}_n(\mathbb{C})/C_k$, where $k$ divides $n$. Let $W$ denote the W
Externí odkaz:
http://arxiv.org/abs/1611.05218