Dualities and Representations of Lie Superalgebras

Cheng, Shun‐Jen; Wang, Weiqiang

doi:10.1090/gsm/144

Cited by 277 publications

(412 citation statements)

References 26 publications

Supporting

Mentioning

405

Contrasting

Unclassified

Order By: Relevance

“…The characters of compact representations are, correspondingly, the Schur symmetric polynomials s λ (x) and Schur supersymmetric polynomials s λ (x|y), where λ is a Young diagram, see e.g. [59]. Schur polynomials form a ring …”

Section: Jhep12(2016)044mentioning

confidence: 99%

See 1 more Smart Citation

T-system on T-hook: Grassmannian solution and twisted Quantum Spectral Curve

Казаков

Leurent

Volin

2016

J. High Energ. Phys.

211

View full text Add to dashboard Cite

Abstract:We propose an efficient grassmannian formalism for solution of bi-linear finitedifference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of gl(K 1 , K 2 |M ) superalgebra. The formalism is inspired by the quantum fusion procedure known from the integrable spin chains and is based on exterior forms of Baxter-like Q-functions. We find a few new interesting relations among the exterior forms of Q-functions and reproduce, using our new formalism, the Wronskian determinant solutions of Hirota equations known in the literature. Then we generalize this construction to the twisted Q-functions and demonstrate the subtleties of untwisting procedure on the examples of rational quantum spin chains with twisted boundary conditions. Using these observations, we generalize the recently discovered, in our paper with N. Gromov, AdS/CFT Quantum Spectral Curve for exact planar spectrum of AdS/CFT duality to the case of arbitrary Cartan twisting of AdS 5 ×S 5 string sigma model. Finally, we successfully probe this formalism by reproducing the energy of gamma-twisted BMN vacuum at single-wrapping orders of weak coupling expansion.

show abstract

Section: Jhep12(2016)044mentioning

confidence: 99%

“…59 This will be possible under mild assumption of existence of generic solutions for T-functions. For instance, in section 2.6.3, we had to assume that the Baxter equation had N independent solutions, and that the functions 1/Ta,s were well defined.…”

Section: B1 Large Bethe Roots and Zeros Of Laguerre Polynomialsmentioning

confidence: 99%

T-system on T-hook: Grassmannian solution and twisted Quantum Spectral Curve

Казаков

Leurent

Volin

2016

J. High Energ. Phys.

211

View full text Add to dashboard Cite

show abstract

“…[8]). Moreover, the decomposition in Theorem 2.8 includes other Howe dualities of type A which have been studied in [1,2,3,5,8,10,11] under suitable choices of A and B (see [12] for more details).…”

Section: And the Irreducible Character Chl(λ)mentioning

confidence: 99%

Jacobi-Trudi Type Formula for Parabolically Semistandard Tableaux

Kim¹

2015

The Pure and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…There is a parity reversing functor Π on the category of vector superspaces (see [8]): For a vector superspace V = V0 ⊕ V1, we let…”

Section: Lemma 25mentioning

confidence: 99%

Simple Harish-Chandra supermodules over the super Schrödinger algebra

2015

View full text Add to dashboard Cite

We study the N = 1 super Schrödinger algebra S in (1 + 1)-dimensional spacetime. The first part of this paper determines the necessary and sufficient conditions for highest weight supermodules over S to be simple. The paper also describes the structure of all Verma supermodules and determines all simple Harish-Chandra supermodules over S. Keywordssuper Schrödinger algebra, weight supermodule, simple supermodule, Harish-Chandra supermodules MSC(2010) 17B10, 17B65, 17B68Citation: Cai Y A, Gao Y, Wang Y J. Simple Harish-Chandra supermodules over the super Schrödinger algebra.

show abstract

Dualities and Representations of Lie Superalgebras

Cited by 277 publications

References 26 publications

T-system on T-hook: Grassmannian solution and twisted Quantum Spectral Curve

T-system on T-hook: Grassmannian solution and twisted Quantum Spectral Curve

Jacobi-Trudi Type Formula for Parabolically Semistandard Tableaux

Simple Harish-Chandra supermodules over the super Schrödinger algebra

Contact Info

Product

Resources

About