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In this paper we verify the local Langlands correspondence for pure inner forms of unramified p-adic groups and tame Langlands parameters in “general position”. For each such parameter, we explicitly construct, in a natural way, a finite set (“L-packet”) of depth-zero supercuspidal representations of the appropriate p-adic group, and we verify some expected(More)
An affine Hecke algebra H contains a large abelian subalgebra A spanned by the Bernstein-Zelevinski-Lusztig basis elements θx, where x runs over (an extension of) the root lattice. The center Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace (“evaluation at the identity”) of the affine Hecke algebra can be written as integral(More)
Department of Mathematics, University of Oklahoma, Norman, OK 73019 Department of Mathematics, University of South Carolina, Columbia, SC 29208 Department of Mathematics, University of Oklahoma, Norman, OK 73019 Abstract. Stationary processes of k-flats in Ed can be thought of as point processes on the Grassmannian L k of k-dimensional subspaces of Ed . If(More)
We study the restriction of minuscule representations to the principal SL2, and use this theory to identify an interesting test case for the Langlands philosophy of liftings. In this paper, we review the theory of minuscule co-weights λ for a simple adjoint group G over C, as presented by Deligne [D]. We then decompose the associated irreducible(More)
Let G be a reductive algebraic group over the local field k. The local Langlands conjecture predicts that the irreducible complex representations π of the locally compact group G(k) can be parametrized by objects of an arithmetic nature: homomorphisms φ from the Weil-Deligne group of k to the complex L-group of G, together with an irreducible representation(More)
Let X be a graph, with corresponding simply-laced Coxeter group W . Then W acts naturally on the lattice L spanned by the vertices of X, preserving a quadratic form. We give conditions on X for the form to be nonsingular modulo two, and study the images of W −→ O(L/2kL). Introduction — This paper investigates the tower of 2-power congruence subgroups in a(More)
An automorphism σ of a simple finite dimensional complex Lie algebra g is called torsion, if σ has finite order in the group Aut(g) of all automorphisms of g. The torsion automorphisms of g were classified by Victor Kac in [12], as an application of his results on infinite dimensional Lie algebras. Those torsion automorphisms contained in the identity(More)
We introduce a new approach to the representation theory of reductive p-adic groups G, based on the Geometric Invariant Theory (GIT) of Moy-Prasad quotients. Stable functionals on these quotients are used to give a new construction of supercuspidal representations of G having small positive depth, called epipelagic. With some restrictions on p, we classify(More)