# On the one-dimensional representations of the general linear supergroup

@article{Trishin2010OnTO, title={On the one-dimensional representations of the general linear supergroup}, author={Ivan M. Trishin}, journal={arXiv: Representation Theory}, year={2010} }

Because of its multiplicativity, the Berezinian is the character of the one-dimensional representation of the general linear supergroup. We give an explicit construction of this representation on a space of tensors. Similarly, we construct the representation such that its character is the inverse of the Berezinian.

## References

SHOWING 1-6 OF 6 REFERENCES

### On reduction of elements of the full matrix superalgebra to a block-diagonal form by conjugation

- Mathematics
- 2002

### Identical relations for the forms with a Young symmetry

- Mathematics
- 1993

Let there be given a Young symmetrizere ℐ. Consider the space of multilinear forms obtained by actione ℐ. In the paper the characteristic property in terms of identities is found for a multilinear…

### Berezinians, Exterior Powers and Recurrent Sequences

- Mathematics
- 2005

We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations…

### Introduction to Superanalysis

- Mathematics
- 1987

1. Grassmann Algebra.- 2. Superanalysis.- 3. Linear Algebra in Z2-Graded Spaces.- 4. Supermanifolds in General.- 5. Lie Superalgebras.- 1. Lie Superalgebras.- 2. Lie Supergroups.- 3. Laplace-Casimir…

### The classical groups : their invariants and representations

- Mathematics
- 1940

In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from…