From Laplace to Langlands via representations of orthogonal groups

By B. Gross, Mark Reeder. 2006

47 citations recorded by the source corpus.

In the late 1960s, Robert Langlands proposed a new and far-reaching connection between the representation theory of Lie groups over real and p-adic fields, and the structure of the Galois groups of these fields [24]. Even though this local Langlands correspondence remains largely conjectural, the relation that it predicts between representation theory and number theory has profoundly changed our views of both fields. Moreover, we now know enough about the correspondence to address, and sometimes solve, traditional problems in representation theory that were previously inaccessible. Roughly speaking, the local Langlands correspondence predicts that complex irreducible representations of a reductive group G over a local field k should be

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a4fdb847dc8e9e896e3e69bf605c66168ddc17f

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In Geometry and Topology

1. E. Vasserot
2. Mark Reeder
3. B. Gross
4. W. Gan
5. Dipendra Prasad
6. M. Varagnolo
7. Stephen Debacker
8. Tasho Kaletha

In Mathematical Physics

1. Mark Reeder
2. W. Gan
3. E. Vasserot
4. Dipendra Prasad
5. B. Gross
6. M. Varagnolo
7. Tasho Kaletha
8. Stephen Debacker

Citations in the corpus

• Arithmetic invariants of discrete Langlands parameters (2010, background): “For example, the corr espondence discussed in [ 10] and [21] involvesH(1)(k,G0), which parametrizes the pure inner forms of the quasi-split groupG0.”
• Multiplicity one Theorems (2007, unknown): “fact the special orthogonal group) this question has been studied by B. Gross and D.Prasad ([G-P],[Pra-2]) who formulated a precise conjecture. An up to date account is given by B.Gross and M.Reeder ([G-R]). In a different setup, in their work on ”Shintani” functions A.Murase and T.Sugano obtained co”
• Depth-zero supercuspidal L-packets and their stability (2009, background): “Our L-packets are also consistent with the conjectures of B. Gross and D. Prasad on restriction from SO2n+1 to SO2n [24].”
• Finite dimensional representations of DAHA and affine Springers fibers : the spherical case (2007, background): “hesis). This classification involves interesting combinatorial objects which already appear in local Langlands correspondence for p-adic groups. See [R2], [R3] for the combinatorial aspects, and [R4], [GR], [DR] for the representation theoretic aspects. Affine Hecke algebras are related to unramified La”
• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups (2009, background): “Since then, there has been considerable progress in the local case [ GR , GW] as well as in the global case [GJR], but the conjecture remains open in general.”
• Restrictions of representations of classical groups: examples (2009, background): “χ(fj) = (−1)nij . where mij = #{r: ai+br>0 >aj+br} nij = #{r: bi+ar>0 >bj+ar}. Since we know how to describe the representations in the L-packets of discrete series parameters when k0 = R [GR], the calculation of χ(ei)χ(ej) and χ(fi)χ(fj) allows us to say something about the representati”