The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G2 over a p-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6 orPGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3. This corresponden...

Let G be a connected reductive linear algebraic group over C and let (ρ, V ) be a regular representation of G . There is a locally finite representation (ρ̂,C[V ]) on the affine algebra C[V ] of V defined by ρ̂(g)f(v) = f(g−1v) for f ∈ C[V ] . Since G is reductive, (ρ̂,C[V ]) decomposes as a direct sum of irreducible regular representations of G . The representation (ρ, V ) is said to be multiplic...

The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G2 over a p-adic field, one can associate a generic supercuspidal irreducible representation of either PGSp6 orPGL3. We prove this conjectural dichotomy, demonstrating a precise correspondence between certain representations of G2 and other representations of PGSp6 and PGL3 when p 6= 2. This ...

Let E be a connected reductive algebraic group over C and let W be its Weyl group. The Springer correspondence allows us to parametrize the irreducible representations E of W as F = F^^ where u is a unipotent element in G (up to conjugacy) and <p is an irreducible representation of the group of components AH(u) = ZH(u)IZ°H(u). (However, not all <p arise in the parametrization.) For F = F^Uttp) ...

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite-dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the weight space structure of finite-dimensional modules for the affine Hecke algebra. Using these indexing sets we show that (1) irreducible calibrated representa...

DRAFT VERSION The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We sh...

Logic programs under Answer Sets semantics can be studied, and actual computation can be carried out, by means of representing them by directed graphs. Several reductions of logic programs to directed graphs are now available. We compare our proposed representation, called Extended Dependency Graph, to the Block Graph representation recently defined by Linke [ 14]. On the relevant fragment of W...

Given a unitary representation T of a finite group G in C, write M for the variety of such representations which are unitary equivalent to T . The representation T is said to be frequent if the dimension of the variety M is maximal (among all representations of G in the same complex space). We prove that the irreducible representations are distributed, in the frequent representation (of large d...

§1. Representations of finite groups 1 §1.1. Definition and Examples 1 §1.2. G-modules 3 §1.3. Mashke’s Theorem 4 §1.4. Schur’s Lemma 6 §1.5. One-dimensional representations 7 §1.6. Exercises 9 §2. Irreducible representations of finite groups 10 §2.1. Characters 10 §2.2. Basic operations on representations and their characters 11 §2.3. Schur’s orthogonality relations 12 §2.4. Decomposition of t...

Let G be the universal cover of the group of automorphisms of a symmetric tube domain and let P = L N be its Shilov boundary parabolic subgroup. This paper attaches an irreducible unitary representation of G to each of the (finitely many) L-orbits on n*. The Hilbert space of the representation consists of functions on the orbit which are square-integrable with respect to a certain L-equivariant...