相关论文: Abstract Young Pairs for Signed Permutation Groups

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of…

We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$…

The classical relativistic linear AAD interaction, introduced by the author, leads in the case of weak coupling to a pointlike particle capable to be sub- mitted to quantization via Feynman's path integrals along the line adequate to the…

For classical groups we show the isomorphism of the Knapp-Stein $R$-group, which describes the structure of parabolically induced representations, and the Arthur $R$-group of the parameter associated to the inducing representation by the…

Within this research, two combinatorial bijections using Young diagrams were studied. The first is a special case of a bijective correspondence between two classes of combinatorial objects. Its proof, based on Young diagrams, establishes…

In this paper we make a clear relationship between the automorphic representations and the quantization through the Geometric Langlands Correspondence. We observe that the discrete series representation are realized in the sum of…

An abstract simplicial complex is said to be $d$-representable if it records the intersection pattern of a collection of convex sets in $\mathbb{R}^d$. In this paper, we show that $d$-representability of a simplicial complex is equivalent…

A classic result of representation theory is Brauer's construction of a diagrammatical (geometrical) algebra whose matrix representation is a certain given matrix algebra, which is the commutating algebra of the enveloping algebra of the…

Let K be the diagonal subgroup of U(2)^{(x)n}. We may view the one-qubit state-space H_1 as a standard representation of U(2) and the n-qubit state space H_n=(H_1)^{(x) n} as the n-fold tensor product of standard representations.…

In this paper we complete our construction of frame-like gauge invariant description for massive mixed symmetry tensor fields corresponding to arbitrary Young tableau with two rows started in [1]. We consider general massive theory in (A)dS…

Abstraction is the process of extracting the essential features from raw data while ignoring irrelevant details. It is well known that abstraction emerges with depth in neural networks, where deep layers capture abstract characteristics of…

In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…

Artin's representation is an injective homomorphism from the braid group $B_n$ on $n$ strands into $\operatorname{Aut}\mathbb{F}_n$, the automorphism group of the free group $\mathbb{F}_n$ on $n$ generators. The representation induces maps…

A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local field is presented. The parametrization is…

This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x-y<=c) and (+/-x<=c), where x and y are variables values and c is an integer or…

We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of…

In this paper we study random representations of fundamental groups of surfaces into special unitary groups. The random model we use is based on a symplectic form on moduli space due to Atiyah, Bott, and Goldman. Let $\Sigma_{g}$ denote a…

Let $D$ be a simple derivation of the polynomial ring $\mathbb{k}[x_1,\dots,x_n]$, where $\mathbb{k}$ is an algebraically closed field of characteristic zero, and denote by…

The symmetric group S_n possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of S_n itself, coincide with the irreducible representations of a certain algebra A_n.…

The asymptotics of the "strip" sums $S_\ell^{(\al)}(n)$ and of their $d$-sums generalizations $T_{d,ds}^{(\al)}(dm)$ (see Definition~\ref{definition1}) were calculated in~\cite{regev}. It was recently noticed that when $d>1$ there is a…