Classification of unipotent representations of simple \(p\)-adic groups. II. (English) Zbl 1016.22011
[Part I in Int. Math. Res. Not. 1995, No. 11, 517-589 (1995; Zbl 0872.20041).]
Let \(K\) be a nonarchimedean local field and let \(G(K)\) be the group of \(K\)-rational points of a connected, adjoint simple algebraic group \(G\) defined over \(K\) which becomes split over an unramified extension of \(K\). Denote by \(U(G(K))\) the set of isomorphism classes of unipotent representations of \(G(K)\). Further, let \(H\) be a simply connected almost simple algebraic group over \(C\) of the type dual to that of \(G\) and denote by \(\theta\): \(G \rightarrow G\) the “graph automorphism” of \(H\) associated to the \(K\)-rational structure of \(G\). The author classifies the unipotent representations of \(G(K)\). More precisely, one of the main results of this paper is the construction of a bijection between \(U(G(K))\) and a set of parameters defined in terms of \(H\) and \(\theta\).
Let \(K\) be a nonarchimedean local field and let \(G(K)\) be the group of \(K\)-rational points of a connected, adjoint simple algebraic group \(G\) defined over \(K\) which becomes split over an unramified extension of \(K\). Denote by \(U(G(K))\) the set of isomorphism classes of unipotent representations of \(G(K)\). Further, let \(H\) be a simply connected almost simple algebraic group over \(C\) of the type dual to that of \(G\) and denote by \(\theta\): \(G \rightarrow G\) the “graph automorphism” of \(H\) associated to the \(K\)-rational structure of \(G\). The author classifies the unipotent representations of \(G(K)\). More precisely, one of the main results of this paper is the construction of a bijection between \(U(G(K))\) and a set of parameters defined in terms of \(H\) and \(\theta\).
Reviewer: Leonid Kurdachenko (Dnepropetrovsk)
MSC:
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
| 20G25 | Linear algebraic groups over local fields and their integers |
Citations:
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