We present and prove the Weyl-Kac type character formula for the irreducible highest weight modules over Borcherds-Bozec superalgebras with dominant integral highest weights.

1.
V. G.
Kac
, “
Simple irreducible graded Lie algebras of finite growth
,”
Math. USSR-Izv.
2
,
1271
1311
(
1968
).
2.
R. V.
Moody
, “
A new class of Lie algebras
,”
J. Algebra
10
,
211
230
(
1968
).
3.
V. G.
Kac
, “
Infninite dimensional Lie algebras and Dedekind’s η-function
,”
Funct. Anal. Appl.
8
,
68
70
(
1974
).
4.
R. E.
Borcherds
, “
Generalized Kac-Moody algebras
,”
J. Algebra
115
,
501
512
(
1988
).
5.
R. E.
Borcherds
, “
Monstrous moonshine and monstrous Lie superalgebras
,”
Invent. Math.
109
,
405
444
(
1992
).
6.
T.
Bozec
, “
Quivers with loops and perverse sheaves
,”
Math. Ann.
362
,
773
797
(
2015
).
7.
T.
Bozec
, “
Quivers with loops and generalized crystals
,”
Compos. Math.
152
,
1999
2040
(
2016
).
8.
T.
Bozec
,
O.
Schiffmann
, and
E.
Vasserot
, “
On the number of points of nilpotent quiver varieties over finite fields
,”
Ann. Sci. Ec. Norm. Super.
53
,
1501
1544
(
2020
).
9.
V. G.
Kac
, “
Lie superalgebras
,”
Adv. Math.
26
,
8
96
(
1977
).
10.
V. G.
Kac
, “
Infinite-dimensional algebras, Dedekind's η-function, classical möbius function and the very strange formula
,”
Adv. Math.
30
,
85
136
(
1978
).
11.
U.
Ray
, “
A character formula for generalized Kac-Moody superalgebras
,”
J. Algebra
177
,
154
163
(
1995
).
12.
S.-J.
Kang
, “
Borcherds–Bozec algebras, root multiplicities and the Schofield construction
,”
Commun. Contemp. Math.
21
,
1850031
(
2019
).
13.
Z.
Fan
,
S.-J.
Kang
,
Y. R.
Kim
, and
B.
Tong
, “
Classical limit of quantum Borcherds-Bozec algebras
,”
J. Pure Appl. Algebra
225
,
106502
(
2021
).
14.
V. G.
Kac
,
Infinite-dimensional Lie Algebras
(
Cambridge University Press
,
1990
).
You do not currently have access to this content.