TY - JOUR

T1 - Construction of Kac - Moody superalgebras as minimal graded Lie superalgebras and weight multiplicities for Kac - Moody superalgebras

AU - Kim, Jeong Ah

AU - Shin, Dong Uy

PY - 2000/7

Y1 - 2000/7

N2 - We construct a Kac-Moody superalgebra ℒ as the minimal graded Lie superalgebra with local part V* ⊕ ge ⊕ V, where g is a "smaller" Lie superalgebra inside ℒ, V is an irreducible highest weight g-module, and V* is the contragredient of V. We show that the weight multiplicities of irreducible highest weight modules over Kac-Moody superalgebras of finite type and affine type [more precisely, Kac-Moody superalgebras of type B(0,r), B(1)(0,r), A(4)(2r,0), A(2)(2r-1,0), and C(2)(r + 1)] are given by polynomials in the rank r. The degree of these weight multiplicity polynomials are less than or equal to the depth of weights.

AB - We construct a Kac-Moody superalgebra ℒ as the minimal graded Lie superalgebra with local part V* ⊕ ge ⊕ V, where g is a "smaller" Lie superalgebra inside ℒ, V is an irreducible highest weight g-module, and V* is the contragredient of V. We show that the weight multiplicities of irreducible highest weight modules over Kac-Moody superalgebras of finite type and affine type [more precisely, Kac-Moody superalgebras of type B(0,r), B(1)(0,r), A(4)(2r,0), A(2)(2r-1,0), and C(2)(r + 1)] are given by polynomials in the rank r. The degree of these weight multiplicity polynomials are less than or equal to the depth of weights.

UR - http://www.scopus.com/inward/record.url?scp=0034413217&partnerID=8YFLogxK

U2 - 10.1063/1.533388

DO - 10.1063/1.533388

M3 - Article

AN - SCOPUS:0034413217

SN - 0022-2488

VL - 41

SP - 4981

EP - 5001

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 7

ER -