Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models
نویسندگان
چکیده
There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of nonzero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit.
منابع مشابه
Monomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملq-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebras and root vectors and which make it possible to construct representations by operators acting according to Gel’fand–Tsetlin-type formulas. Unitary representations of the q-deformed algebras Uq(son,1) are found. AMS subject classifications (1980). 16...
متن کاملQuasifinite representations of classical Lie subalgebras of W 1 + ∞
We show that there are precisely two, up to conjugation, anti-involutions σ± of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight representations of the central extension D̂± of the Lie subalgebra of this algebra fixed by −σ±, and find the unitary ones. We realize them in terms of highest weight represen...
متن کاملThe paraboson Fock space and unitary irreducible representations of the Lie superalgebra osp(1|2n)
It is known that the defining relations of the orthosymplectic Lie superalgebra osp(1|2n) are equivalent to the defining (triple) relations of n pairs of paraboson operators b i . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V (p) of osp(1|2n). Apart from the s...
متن کاملThe Virasoro algebra and its representations in physics
In this report for the course “Lie algebras and quantum groups” at KTH I discuss the origin of the Virasoro algebra, give the physical motivation for studying its unitary irreducible highest weight representations, and examine the necessary and sufficient conditions for such representations to exist.
متن کامل