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Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect representation theoretic properties on function spaces, with focus on multiplicities and spectrum.
Let $F$ be either $mathbb{R}$ or a finite extension of $mathbb{Q}_p$, and let $G$ be a finite central extension of the group of $F$-points of a reductive group defined over $F$. Also let $pi$ be a smooth representation of $G$ (Frechet of moderate gro
We investigate the structure and properties of an Artinian monomial complete intersection quotient $A(n,d)=mathbf{k} [x_{1}, ldots, x_{n}] big / (x_{1}^{d}, ldots, x_{n}^d)$. We construct explicit homogeneous bases of $A(n,d)$ that are compatible wit
The paper proves an identity involving Weil indices and epsilon factors for a local field. The starting point is a pair consisting of a reductive group and a maximal torus.
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the
We introduce graded Hecke algebras H based on a (possibly disconnected) complex reductive group G and a cuspidal local system L on a unipotent orbit of a Levi subgroup M of G. These generalize the graded Hecke algebras defined and investigated by Lus