For a real or p-adic connected reductive group G, Harish-Chandra introduced the Plancherel measure on the tempered dual Ĝtemp and founded the Plancherel formula [7, 18] relating functions on G to functions on Ĝtemp. While the Plancherel measure is equal to the formal degree for square-integrable representations, there has been no similar interpretation for tempered but nonsquare-integrable repr...

We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are e...

Clifford analysis offers a higher dimensional function theory studying the null solutions of the rotation invariant, vector valued, first order Dirac operator ∂. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂J , leading to the system of equations...

Using the sharpened Helgason–Johnson bound, this paper classifies all irreducible unitary representations with non-zero Dirac cohomology of E7(−5). As an application, we find that cancellation between even part and odd continues to happen for certain Assuming infinitesimal character being integral, further improve bound This should help people understand (part of) dual group.

0.1. Let Γ be a finite subgroup of SU(2). The question we will deal with in this paper is how an arbitrary (unitary) irreducible representation of SU(2) decomposes under the action of Γ. The theory of McKay assigns to Γ a complex simple Lie algebra g of type A−D−E. The assignment is such that if Γ̃ is the unitary dual of Γ we may parameterize Γ̃ by the nodes (or vertices) of the extended Coxeter-...

New path description for the M(k + 1, 2k + 3) models and the dual Z k graded parafermions ABSTRACT We present a new path description for the states of the non-unitary M(k + 1, 2k + 3) models. This description differs from the one induced by the Forrester-Baxter solution, in terms of configuration sums, of their restricted-solid-on-solid model. The proposed path representation is actually very s...

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.

Leptin’s theorem asserts that a locally compact group is amenable if and only if its Fourier algebra has a bounded (by one) approximate identity. In the language of locally compact quantum groups—in the sense of J. Kustermans and S. Vaes—, it states that a locally compact group is amenable if and only if its quantum group dual is co-amenable. It is an open problem whether this is true for gener...

Let lambda be a partition, with l parts, and let F(lambda) be the irreducible finite dimensional representation of GL(m) associated to lambda when l < or = m. The Littlewood Restriction Rule describes how F(lambda) decomposes when restricted to the orthogonal group O(m) or to the symplectic group Sp(m2) under the condition that l < or = m2. In this paper, this result is extended to all partitio...