相关论文: Character States and Generator Matrix Elements for…

A new set of polynomial states (to be called character states) are derived for $Sp(4)$ reduced to its $SU(2) \times U(1)$ subgroup, and the relevant generator matrix elements are evaluated for generic representations $(a,b)$ of $Sp(4)$.…

Basis states and generator matrix elements are given for the generic representation $(a,b)$ of $G_2$ in an $SU(3)$ basis.

We consider decomposition of coordinate independent states into SO(9)xSU(2) representations in SU(2) Matrix theory. To see what and how many representations appear in the decomposition, we compute the character, which is given by a trace…

In this manuscript we study the Double SU(4) model as a grand unified theory based on the gauge group $\,SU(4)\times SU(4)\left(\times \mathcal{Z}_2\right)$. A complete set of generators is constructed according to a pattern of symmetry…

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in…

In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…

This paper obtains the matrix elements and characters of the discrete series unitary irreducible representations (UIRs) of the Sp$(4,\mathbb{R})$ group. With an isomorphic relationship to the two-fold covering of SO$_0(2,3)$…

A new set of $ h(1) \oplus su(2)$ vector algebra eigenstates on the matrix domain is obtained by defining them as eigenstates of a generalized annihilation operator formed from a linear combination of the generators of this algebra which…

In this mostly expository article, elements of higher category theory essential to the construction of a class of four dimensional quantum geometric models are reviewed. These models improve current state sum models for Quantum Gravity,…

Character sumrules associated with the realization of the $N=4$ superconformal algebra $\At$ on manifolds corresponding to the group cosets $SU(3)_{\ktp }/U(1)$ are derived and developed as an important tool in obtaining the modular…

We discuss the group theory relevant to the ground-state baryons in large N_c QCD. For very large representation, the group generators become classical variables. We find the form of the classical generators for the completely symmetric N…

We study various aspects of parafermionic theories such as the precise field content, a description of a basis of states (that is, the counting of independent states in a freely generated highest-weight module) and the explicit expression…

We study the discrete state structure of $\hat c=1$ superconformal matter coupled to 2-D supergravity. Factorization properties of scattering amplitudes are used to identify these states and to construct the corresponding vertex operators.…

The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…

Turull has described the fields of values for characters of $SL_n(q)$ in terms of the parametrization of the characters of $GL_n(q)$. In this article, we extend these results to the case of $SU_n(q)$.

Parametrization of qutrits on the complex projective plane CP^2 = SU(3)/U(2) is given explicitly. A set of constraints that characterize mixed state density matrices is found.

We study a spectral problem related to the finite-dimensional characters of the groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$, which form the classical series $C$, $B$, and $D$, respectively. The irreducible characters of these three series are…

Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of…

Let $U(q)$ be a Sylow $p$-subgroup of the Chevalley groups $D_4(q)$ where $q$ is a power of a prime $p$. We describe a construction of all complex irreducible characters of $U(q)$ and obtain a classification of these irreducible characters…

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete…