A <i>q</i>-superdimension formula for irreps of type I quantum superalgebras

This paper describes a method to obtain state model parameters for an infinite series of Links-Gould link invariants LG m,n , based on quantum R matrices associated with the (0m |αn) representations of the quantum superalgebras Uq[gl(m|n)]. Explicit details of the state models for the cases n = 1 and m = 1, 2, 3, 4 are supplied. Some gross properties of the link invariants are provided, as well as some explicit evaluations. * RIMS, Kyoto University 606-8502, Japan. ddw@kurims. kyoto-u.ac.jp Corresponding to each finite dimensional highest weight representation of each quantum superalgebra, there exists a quantum link invariant (LG), originally described in [17]. These invariants are similar to those associated with the usual (i.e. ungraded) quantum algebras (e.g. [10,11,23]), although there are some technical differences.Here, we describe the construction of parameters for state models for evaluating a class of these invariants. Specifically, we will define LG m,n to be the quantum link invariant associated with the representation π ≡ π Λ of highest weight Λ = (0 m |α n ), of the quantum superalgebra U q [gl(m|n)]. To do so, we first broadly introduce the algebraic structures, then we briefly review the terminology used to describe state model parameters, and finally, we look at the construction of specific state model parameters for our particular class of representations.The reader will have by now appreciated the recurring patterns in the components of our R matrices. To save space, we introduce a little more notation, which eliminates the q brackets altogether. To whit, we write:where z ∈ { 1 2 , 1}, and i ∈ {0, 1, 2, 3}. With this notation, the braid generator σ has 758 nonzero components: q

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A q-superdimension formula for irreps of type I quantum superalgebras

Cited by 3 publications

References 35 publications

Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)

Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)

Eigenvalues of Casimir invariants for unitary irreps of

An Infinite Suite of Links–Gould Invariants

Contact Info

Product

Resources

About