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Documents  22E50 | enregistrements trouvés : 9

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Spherical Hecke algebra, Satake transform, and an introduction to local Langlands correspondence.

20C08 ; 22E50 ; 11S37

Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it pertains to these terms. Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it ...

11F66 ; 22E50 ; 22E55

Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in which we aim to classify all non-trivial extensions between these modules and to compare them with their analogues for $p$-modular smooth representations of $SL_2(F)$ and with their Galois counterpart in the setting of the local Langlands correspondences in natural characteristic. Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in ...

11F70 ; 11F85 ; 20C08 ; 20G05 ; 22E50

We prove a finiteness result on the $p$-adic cohomology of the Lubin-Tate tower, which allows one to go from mod $p$ and $p$-adic
$GL_n (F)$-representations to Galois representations (compatibly with some global cor-respondences).

14G22 ; 22E50 ; 14F30

Let G be a connected reductive p-adic group that splits over a tamely ramified extension. Let H be the fixed points of an involution of G. An irreducible smooth H-distinguished representation of G is H-relatively supercuspidal if its relative matrix coefficients are compactly supported modulo H Z(G). (Here, Z(G) is the centre of G.) We will describe some relatively supercuspidal representations whose cuspidal supports belong to the supercuspidals constructed by J.K. Yu. Let G be a connected reductive p-adic group that splits over a tamely ramified extension. Let H be the fixed points of an involution of G. An irreducible smooth H-distinguished representation of G is H-relatively supercuspidal if its relative matrix coefficients are compactly supported modulo H Z(G). (Here, Z(G) is the centre of G.) We will describe some relatively supercuspidal representations whose cuspidal supports belong to the supe...

22E50 ; 22E35

The local Gan-Gross-Prasad conjectures concern certain branching or restriction problems between representations of real or p-adic Lie groups. In its simplest form it predicts certain multiplicity-one results for "extended" L-packets. In a recent series of papers, Waldspurger has settled the conjecture for special orthogonal groups over p-adic field. In this talk, I will present a proof of the conjecture for unitary groups which has the advantage of working equally well over archimedean and non-archimedean fields. The local Gan-Gross-Prasad conjectures concern certain branching or restriction problems between representations of real or p-adic Lie groups. In its simplest form it predicts certain multiplicity-one results for "extended" L-packets. In a recent series of papers, Waldspurger has settled the conjecture for special orthogonal groups over p-adic field. In this talk, I will present a proof of the conjecture for unitary groups which has the ...

22E50 ; 11F85

In joint work with Hiraku Atobe, we determine the theta lifting of irreducible tempered representations for symplectic-metaplectic­orthogonal and unitary dual pairs in terms of the local Langlands correspondence. The main new tool for proving our result is the recently established local Gross-Prasad conjecture.

11F27 ; 11F70 ; 22E50

This is a joint work with J. Cogdell and T.-L. Tsai. I will report on the progress made in proving the equality of Artin epsilon factors for exterior and symmetric square L-functions with those on the representation theoretic side through the local Langlands correspondence. The equality for L-functions has already been established by Henniart. I will show how the equality can be proved if one has the stability of these factors under highly ramified twists for supercuspidal representations. I will then discuss the stability question for supercuspidals by discussing how it can be deduced from a generalization of germ expansions of Jacquet and Ye from Bessel functions to certain partial Bessel functions. I will elaborate by explaining the stability in the case of GL(2) through general lemmas proved so far. This is a joint work with J. Cogdell and T.-L. Tsai. I will report on the progress made in proving the equality of Artin epsilon factors for exterior and symmetric square L-functions with those on the representation theoretic side through the local Langlands correspondence. The equality for L-functions has already been established by Henniart. I will show how the equality can be proved if one has the stability of these factors under highly ...

11F66 ; 11F70 ; 11F80 ; 22E50

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