TY - JOUR

T1 - Solutions of super Knizhnik–Zamolodchikov equations

AU - Cao, Bintao

AU - Lam, Ngau

N1 - Funding Information:
The first author was partially supported by NSFC (Grant Nos. 11571374, 11521101 and 11771461). A part of this research was done during the visit of the second author to Sun Yat-sen University. The second author was partially supported by Ministry of Science and Technology Grant 107-2115-M-006-005-MY2 of Taiwan and he thanks Sun Yat-sen University for hospitality and support.
Funding Information:
The first author was partially supported by NSFC (Grant Nos. 11571374, 11521101 and 11771461). A part of this research was done during the visit of the second author to Sun Yat-sen University. The second author was partially supported by Ministry of Science and Technology Grant 107-2115-M-006-005-MY2 of Taiwan and he thanks Sun Yat-sen University for hospitality and support.
Publisher Copyright:
© 2020, Springer Nature B.V.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - We establish an explicit bijection between the sets of singular solutions of the (super) KZ equations associated with the Lie superalgebra, of infinite rank, of type a, b, c, d and with the corresponding Lie algebra. As a consequence, the singular solutions of the super KZ equations associated with the classical Lie superalgebra, of finite rank, of type a, b, c, d for the tensor product of certain parabolic Verma modules (resp., irreducible modules) are obtained from the singular solutions of the KZ equations for the tensor product of the corresponding parabolic Verma modules (resp., irreducible modules) over the corresponding Lie algebra of sufficiently large rank, and vice versa. The analogous results for some special kinds of trigonometric (super) KZ equations are obtained.

AB - We establish an explicit bijection between the sets of singular solutions of the (super) KZ equations associated with the Lie superalgebra, of infinite rank, of type a, b, c, d and with the corresponding Lie algebra. As a consequence, the singular solutions of the super KZ equations associated with the classical Lie superalgebra, of finite rank, of type a, b, c, d for the tensor product of certain parabolic Verma modules (resp., irreducible modules) are obtained from the singular solutions of the KZ equations for the tensor product of the corresponding parabolic Verma modules (resp., irreducible modules) over the corresponding Lie algebra of sufficiently large rank, and vice versa. The analogous results for some special kinds of trigonometric (super) KZ equations are obtained.

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U2 - 10.1007/s11005-020-01275-z

DO - 10.1007/s11005-020-01275-z

M3 - Article

AN - SCOPUS:85081300780

SN - 0377-9017

VL - 110

SP - 1799

EP - 1834

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 7

ER -