Construction of Gelfand–Tsetlin Basis for $\mathcal U_q(\textit{gl}(N+1))$-modules

Abstract

The Gelfand-Tsetlin basis for irreducible c U q (gl(N4-1))-modules of finite dimensions is constructed by means of the lowering operators. § 0. IntroductionIn the previous paper [1], we constructed the Gelfand-Tsetlin basis for irreducible "Ug(^/(]V+l))-modules of finite dimensions, in terms of the lowering operators. In this paper, we will give detailed accounts of our construction of this basis.We give the result when q is a non-zero complex variable and not a root of unity, however from the view of technical arguments in its proof we also have to deal with the case of q to be a transcendental element over C.Let

Stress-enhanced ion diffusion at the vicinity of a crack tip as evidenced by atomic force microscopy in silicate glasses

“…A commonly accepted interpretation of this multi-step leaching behavior is that the former is related to a diffusion-controlled process associated with the ion diffusion of Na + and/or H + (or H 3 O + ), and the latter is caused by a chemical reaction at the surface of the glass. For the former process, a few possible mechanisms of diffusion have been proposed: Na self-diffusion from the inside to the outside of the glass [45,46] and interdiffusion of Na + in glass via protons or hydronium ions. However no real consensus has been reached on this matter.…”

Gelfand–Tsetlin modules of quantum gln defined by admissible sets of relations

“…By Theorem 2.11 in [34], any irreducible finite dimensional U q -module is isomorphic to V S (T (v)) for some v. The family of modules {V ∅ (T (v))} coincide with the family of generic modules as constructed in [29], Theorem 2.…”

“…As particular cases of this construction one obtains any irreducible finite dimensional module as in [34], Theorem 2.11, and generic modules as in [29], Theorem 2.…”

Irreducible Generic Gelfand-Tsetlin Modules of gl(n)

“…The purpose of current paper is to study the Gelfand-Tsetlin basis for quantum gl n aiming to generalize the constructions above in the quantum case. Previously, partial results were obtained for example in [21], [23] , [24], [12]. A general theory of Gelfand-Tsetlin modules for quantum gl n was developed in [11].…”