## 53 Citations

### The Kac–Wakimoto character formula for the general linear Lie superalgebra

- Mathematics
- 2015

Character formulas for Lie superalgebras have been shown to have important applications to number theory and combinatorics. We prove the Kac-Wakimoto character formula for the general linear Lie…

### Character formulas and tame representations for gl(m|n)

- Mathematics
- 2014

In 1994, Kac and Wakimoto suggested a generalization of Bernstein and Leites character formula for basic Lie superalgebras, and the natural question was raised: to which simple highest weight modules…

### JACOBI-TRUDI TYPE FORMULA FOR CHARACTER OF IRREDUCIBLE REPRESENTATIONS OF gl(m|1)

- Mathematics
- 2018

We prove a determinantal type formula to compute the irreducible characters of the general Lie superalgebra gl(m|1) in terms of the characters of the symmetric powers of the fundamental…

### O ct 2 01 3 KAC-WAKIMOTO CHARACTER FORMULA FOR THE GENERAL LINEAR LIE SUPERALGEBRA

- Mathematics
- 2018

Character formulas for Lie superalgebras have been shown to have important applications to number theory and combinatorics. We prove the Kac-Wakimoto character formula for the general linear Lie…

### Character and Dimension Formulae for Queer Lie Superalgebra

- Mathematics
- 2015

Closed formulae are constructed for the characters and dimensions of the finite dimensional simple modules of the queer Lie superalgebra $${\mathfrak{q}(n)}$$q(n). This is achieved by refining…

### Generalised Jantzen filtration of exceptional Lie superalgebras

- Mathematics
- 2016

Let g be an exceptional Lie superalgebra, and let p be the maximal parabolic subalgebra which contains the distinguished Borel subalgebra and has a purely even Levi subalgebra. For any parabolic…

### Representations of the general linear Lie superalgebra in the BGG category O

- Mathematics
- 2014

This is a survey of some recent developments in the highest weight repesentation theory of the general linear Lie superalgebra gln|m(C). The main focus is on the analog of the Kazhdan-Lusztig…

## References

SHOWING 1-10 OF 24 REFERENCES

### Character formulae for the lie superalgebra C(n)

- Mathematics
- 1991

Using a recent result on the structure of the maximal sub module of the Kac-module for type I Lie super algebras, we derive two character formulae for all finite-dimensional simple modules of the Lie…

### Dimension formulas for the Lie superalgebra sl(m/n)

- Mathematics
- 1995

Although character formulas for simple finite‐dimensional modules of the Lie superalgebra sl(m/n) are not known in general, they are known in the cases of so‐called typical and of singly atypical…

### Kazhdan-Lusztig polynomials and character formula for the Lie superalgebragI(m/n)

- Mathematics
- 1996

We find the character formula for irreducible finite-dimensionalgl(m/n)-modules. Also multiplicities of the composition factors in a Kac module are calculated.

### Characters of irreducibleG-modules and cohomology ofG/P for the lie supergroupG=Q(N)

- Mathematics
- 1997

We prove a character formula for any finite-dimensional irreducible representationV of the “queer” Lie superalgebra g=q(n). It expresses chV in terms of the multiplicities of the irreducible…

### Categories of Finite Dimensional Weight Modules over Type I Classical Lie Superalgebras

- Mathematics
- 1996

Since the generalization of highest weight representation theory to Lie w x w x superalgebras in K1 ] K3 , a number of interesting results on the highest weight representation theory of classical Lie…

### Integrable Highest Weight Modules over Affine Superalgebras and Number Theory

- Mathematics
- 1994

The problem of representing an integer as a sum of squares of integers has had a long history. One of the first after antiquity was A. Girard who in 1632 conjectured that an odd prime p can be…

### Characters and composition factor multiplicities for the Lie superalgebra gl(m/n)

- Mathematics
- 1998

The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of…

### On the composition factors of Kac modules for the Lie superalgebras sl(m/n)

- Mathematics
- 1992

In the classification of finite‐dimensional modules of Lie superalgebras, Kac distinguished between typical and atypical modules. Kac introduced an induced module, the so‐called Kac module V(Λ) with…

### En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

- Mathematics
- 1998

AbstractThe multiplicities aλ μ of simple modules Lμ in the composition series of Kac modules V lambda for the Lie superalgebra
$${\mathfrak{g}}{\mathfrak{l}}$$
(m/n ) were described by Serganova,…