We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenberg-Virasoro algebra, having a nontrivial fi...

The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

The irreducible representations of the symmetric group Sn are parameterized by combinatorial objects called Young diagrams, or shapes. A given irreducible representation has a basis indexed by Young tableaux of that shape. In fact, this basis consists of weight vectors (simultaneous eigenvectors) for a commutative subalgebra F[X] of the group algebra FSn. The double affine Hecke algebra (DAHA) ...

We study quantum chromodynamics (QCD) on a finite lattice Λ in the Hamiltonian approach. First, we present the field algebra AΛ as comprising a gluonic part, with basic building block being the crossed product C∗-algebra C(G) ⊗α G, and a fermionic (CAR-algebra) part generated by the quark fields. By classical arguments, AΛ has a unique (up to unitary equivalence) irreducible representation. Nex...

We prove a version of the Poincaré–Birkhoff–Witt theorem for the twisted quantized enveloping algebra U′q(sp2n). This is a subalgebra of Uq(gl2n) and a deformation of the universal enveloping algebra U(sp2n) of the symplectic Lie algebra. We classify finitedimensional irreducible representations of U′q(sp2n) in terms of their highest weights and show that these representations are deformations ...

A spin system is a sequence of self-adjoint unitary operators U1, U2, . . . acting on a Hilbert space H which either commute or anticommute, UiUj = ±UjUi for all i, j; it is is called irreducible when {U1, U2, . . . } is an irreducible set of operators. There is a unique infinite matrix (cij) with 0, 1 entries satisfying UiUj = (−1) cij UjUi, i, j = 1, 2, . . . . Every matrix (cij ) with 0, 1 e...

We study the representation theory of the W-algebra Wk(ḡ) associated with a simple Lie algebra ḡ at level k. We show that the “−” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k ∈ C. Moreover, we show that the character of each irreducible highest weight representation of Wk(ḡ) is completely determined by that of the corresponding irred...

We describe an algorithmic test, using the “standard polynomial identity” (and elementary computational commutative algebra), for determining whether or not a finitely presented associative algebra has an irreducible n-dimensional representation. When ndimensional irreducible representations do exist, our proposed procedure can (in principle) produce explicit constructions.

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V G-modules which occur as submodules of irreducible V -modules by using intertwining operators for V . We also determine some fusion rules for a vertex operator algebra as an application.