相关论文: On a construction of the basic spin representation…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We determine the minimal polynomial of each element of the double cover $G$ of the symmetric or alternating group in every irreducible spin representation of $G$.

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin-line bundles of the 2-sphere. In particular,…

The analogies between symplectic and orthogonal groups, regarded as symmetries of real bilinear forms, are manifest in their (metaplectic and spin) projective representations. In finite dimensions, those are true representations of doubly…

The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes,…

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions…

We discuss an extension of the quantization method based on the induced representation of the canonical group.

Let G be a connected reductive group over a field of characteristic zero, and consider an orthogonal representation of G. We give a simple criterion for whether the representation lifts to the spin group, in terms of the highest weights of…

We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that…

This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in…

We present a simple group representation analysis of massive, and particularly ``partially massless'', fields of arbitrary spin in de Sitter spaces of any dimension. The method uses bulk to boundary propagators to relate these fields to…

We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for…

In the previous paper, we proposed a practical method of constructing explicitly representation groups $R(G)$ for finite groups $G$, and apply it to certain typical finite groups $G$ with Schur multiplier $M(G)$ containing prime number 3.…

We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures…

In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.

In this paper, we give a construction of certain induced complementary series of the universal covering of the symplectic groups. There are abundant such representations besides those of linear groups. We achieve this by applying invariant…

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper…

The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…