ar X iv : q - a lg / 9 70 80 16 v 1 1 7 A ug 1 99 7 Classification of irreducible modules of W 3 algebra with c = −
نویسنده
چکیده
We construct irreducible modules Vα, α ∈ C over W3 algebra with c = −2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W3 algebra with c = −2. Highest weights of modules Vα, α ∈ C with respect to the full (two-dimensional) Cartan subalgebra of W3 algebra are ( 1 2α(α − 1), 16α(α − 1)(2α − 1) ) . They are parametrized by points (t, w) on a rational curve w2− 19t(8t+1) = 0. Irreducible modules of vertex algebra W1+∞ with c = −1 are also classified.
منابع مشابه
ar X iv : q - a lg / 9 70 80 08 v 1 7 A ug 1 99 7 W 1 + ∞ algebra , W 3 algebra , and Friedan - Martinec - Shenker bosonization
We show that the vertex algebra W1+∞ with central charge −1 is isomorphic to a tensor product of the simple W3 algebra with central charge −2 and a Heisenberg vertex algebra generated by a free bosonic field. We construct a family of irreducible modules of the W3 algebra with central charge −2 in terms of free fields and calculate the full character formulas of these modules with respect to the...
متن کاملar X iv : q - a lg / 9 60 70 31 v 1 3 0 Ju l 1 99 6 Level - 0 action of U q ( ŝl n ) on the q - deformed Fock spaces
On the level-1 Fock space modules of the algebra Uq(ŝln) we define a level-0 action U0 of the Uq(ŝln), and an action of an abelian algebra of conserved Hamiltonians commuting with the U0. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials. e-mail: takemura@kurim...
متن کاملar X iv : q - a lg / 9 70 50 22 v 1 2 7 M ay 1 99 7 Coloured Hopf
Some new algebraic structures related to the coloured Yang-Baxter equation, and termed coloured Hopf algebras, are reviewed. Coloured quantum universal enveloping algebras of Lie algebras are defined in this context. An extension to the coloured graded Yang-Baxter equation and coloured Hopf superalgebras is also presented. The coloured two-parameter quantum universal enveloping algebra of gl(1/...
متن کاملar X iv : q - a lg / 9 70 90 01 v 1 1 S ep 1 99 7 Bilinear identity for q - hypergeometric integrals
متن کامل
ar X iv : q - a lg / 9 70 50 20 v 1 2 7 M ay 1 99 7 QUANTUM GROUP DUALITY AND THE CUNTZ ALGEBRA
The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra Uq(g), and the structure of a co-module algebra over the quantum group Gq associated with Uq(g). These two algebraic structures are dual to each other via the duality between Gq and Uq(g).
متن کامل