Facets of nondegeneracy: central type factor groups, Heisenberg representations and Hadamard matrices

@misc{bieliavsky2026facets,
  title = {{Facets of nondegeneracy: central type factor groups, Heisenberg representations and Hadamard matrices}},
  author = {Pierre Bieliavsky and Victor Gayral and Sergey Neshveyev and Lars Tuset},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11785},
  eprint = {2610.11785},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11785},
}

TY  - UNPB
TI  - Facets of nondegeneracy: central type factor groups, Heisenberg representations and Hadamard matrices
AU  - Pierre Bieliavsky
AU  - Victor Gayral
AU  - Sergey Neshveyev
AU  - Lars Tuset
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.11785
UR  - https://arxiv.org/abs/2610.11785
AB  - Given a pair of complementary subgroups P and N of a finite group G, we first discuss how the same type of functions 𝔼: P× N→ 𝕋, which we call bi-$1$-cocycles, appear naturally in the study of projective representations of G of Heisenberg type and second cohomology of G and of its dual quantum group Ĝ. We show then that such representations are irreducible and the corresponding ordinary and dual $2$-cocycles are nondegenerate if and only if the matrix (𝔼(p,n))_p,n is invertible, if and only if it is Hadamard. We illustrate the result with examples arising from symplectic nilpotent Lie algebras over finite fields with two complementary Lagrangian subalgebras.
ER  -