Related papers: Depth-zero base change for ramified U(2,1)

For a quasi-split classical group over a p-adic field with sufficiently large residual characteristic, we prove that the maximum of depth of representations in each L-packet equals the depth of the corresponding L-parameter. Furthermore,…

We initiate the investigation of critical exponents (in degree equal to the rank) for the vanishing of L^p-cohomology of higher rank Lie groups and related manifolds. We deal with the rank 2 case and exhibit such phenomena for SL$_3$(R) and…

We examine whether it is possible to realize finite groups $G$ as Galois groups of minimally tamely ramified extensions of $\mathbb{Q}$ and also specify both the inertia groups and the further decomposition of the ramified primes.

Let G be any connected reductive group over a non-archimedean local field. We analyse the unipotent representations of G, in particular in the cases where G is ramified. We establish a local Langlands correspondence for this class of…

We prove that $\bar {\mathbb Q}_\ell$-local systems of bounded rank and ramification on a smooth variety $X$ defined over an algebraically closed field $k$ of characteristic $p\neq \ell$ are tamified outside of codimension $2$ by a finite…

We study homological representations of mapping class groups, including the braid groups. These arise from the twisted homology of certain configuration spaces, and come in many different flavours. Our goal is to give a unified general…

We provide a detailed analysis of atomic *-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a direct sum or direct integral of irreducible atomic…

Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…

We find the irreducible decomposition of the Weil representation of the unitary group $\mathrm{U}_{2n}(A)$, where $A$ is a ramified quadratic extension of a finite, commutative, local, principal ideal ring $R$ and the nilpotency degree of…

We prove a geometric version of a classical result on the characterization of an irreducible cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_E)$ being the base change of a stable cuspidal packet of the quasi-split unitary…

We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a…

It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…

In this paper, we describe a stratification on the reduced special fiber of the basic unramified unitary Rapoport-Zink space of signature $(1,n-1)$ and at arbitrary parahoric level. We prove the smoothness, irreducibility and compute the…

Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess numerous applications in quantum information science. It is well-known that in prime power dimensions N=p^m (with p prime and m a positive integer) there exists a…

We give the details of the construction of a map to restate a conjectural expression about adjoint group action on generic representations in L-packets. We give an application of the construction to give another proof of the classification…

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…

Given a simply connected nilpotent Lie group having unitary irreducible representations that are square-integrable modulo the center (SI/Z), we develop a notion of periodization on the group Fourier transform side, and use this notion to…

Let F be a p-adic field with p odd. Quadratic base change and theta-lifting are shown to be compatible for supercuspidal representations of SL(2,F). The argument involves the theory of types and the lattice model of the Weil representation.

In this paper, we establish the explicit lower bound estimates for the rank of universal quadratic forms in some certain families of real cubic fields under the condition of density one. The more general results that represent all multiples…