Young tableaux for the Lie superalgebra OSP(M/N)

2005 ◽  
pp. 53-55
Author(s):  
J. -P. Hunri ◽  
B. Morel ◽  
H. Ruegg ◽  
A. Sciarrino ◽  
A. Sorba
Keyword(s):  
Lie Superalgebra ◽  
Young Tableaux

BOSON–FERMION ALGEBRA AND BOSON–FERMION REPRESENTATION OF LIE SUPERALGEBRA OSP (1, 2)

1992 ◽  
Vol 12 (3) ◽  
pp. 270-281
Author(s):  
Gaojian Zeng
Keyword(s):  
Lie Superalgebra ◽  
Fermion Algebra

scholarly journals Classification of Degenerate Verma Modules for E(5, 10)

2021 ◽  
Author(s):  
Nicoletta Cantarini ◽  
Fabrizio Caselli ◽  
Victor Kac
Keyword(s):  
Infinite Number ◽  
Verma Module ◽  
Lie Superalgebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Finite Dimensional ◽  
De Rham ◽  
Via Classification

AbstractGiven a Lie superalgebra $${\mathfrak {g}}$$ g with a subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 , and a finite-dimensional irreducible $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 -module F, the induced $${\mathfrak {g}}$$ g -module $$M(F)={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {g}}_{\ge 0})}F$$ M ( F ) = U ( g ) ⊗ U ( g ≥ 0 ) F is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra $${\mathfrak {g}}=E(5,10)$$ g = E ( 5 , 10 ) with the subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 of minimal codimension. This is done via classification of all singular vectors in the modules M(F). Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as “exceptional” de Rham complexes for E(5, 10).

scholarly journals Higher spins from exotic dualisations

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nicolas Boulanger ◽  
Victor Lekeu
Keyword(s):  
Infinite Number ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Young Tableaux ◽  
Spacetime Dimension ◽  
Massless Field ◽  
Free Level ◽  
Higher Spins

Abstract At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height hi by columns of height D − 2 − hi, where D is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of D − 2 extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in D = 5 and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in D = 3.

Standard Young tableaux in a (2,1)-hook and Motzkin paths

2021 ◽  
Vol 344 (7) ◽  
pp. 112395
Author(s):  
Rosena R.X. Du ◽  
Jingni Yu
Keyword(s):  
Young Tableaux ◽  
Standard Young Tableaux ◽  
Motzkin Paths

scholarly journals Vicious walkers and hook Young tableaux

2003 ◽  
Vol 36 (12) ◽  
pp. 3033-3048 ◽  
Author(s):  
Kazuhiro Hikami ◽  
Takashi Imamura
Keyword(s):  
Young Tableaux ◽  
Vicious Walkers

scholarly journals Frames, Young tableaux, and Baxter sequences

1977 ◽  
Vol 26 (3) ◽  
pp. 275-289 ◽  
Author(s):  
Glânffrwd P Thomas
Keyword(s):  
Young Tableaux

2-Local superderivations on the Lie superalgebra of Block type

2021 ◽  
pp. 1-16
Author(s):  
Yucai Su ◽  
Xiaoqing Yue ◽  
Xiaoyu Zhu
Keyword(s):  
Lie Superalgebra ◽  
Block Type

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

scholarly journals Gel’fand–Zetlin basis and Clebsch–Gordan coefficients for covariant representations of the Lie superalgebra gl(m∣n)

2010 ◽  
Vol 51 (9) ◽  
pp. 093523 ◽  
Author(s):  
N. I. Stoilova ◽  
J. Van der Jeugt
Keyword(s):  
Lie Superalgebra ◽  
Covariant Representations

scholarly journals On the finite W-algebra for the Lie superalgebra Q(N) in the non-regular case

2017 ◽  
Vol 58 (11) ◽  
pp. 111701 ◽  
Author(s):  
Elena Poletaeva ◽  
Vera Serganova
Keyword(s):  
Lie Superalgebra ◽  
Regular Case
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