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Frobenius forms and semisimplicity of cyclotomic quiver Hecke superalgebras

  • Shuo Li
  • Lei Shi
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Abstract

We determine the Nakayama automorphism of the canonical homogeneous Frobenius form on cyclotomic quiver Hecke superalgebras. We give explicit necessary and sufficient conditions on the dominant weight and the rank for semisimplicity of cyclotomic quiver Hecke superalgebras of types Ae(1), Ce(1), A2e(2), De+1(2), A∞, B∞, and C∞. As an application, we prove that a cyclotomic Hecke--Clifford superalgebra is semisimple if and only if the corresponding Poincaré polynomial is nonzero.

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Cite

BibTeXRIS
BibTeX
@misc{li2026frobenius,
  title = {{Frobenius forms and semisimplicity of cyclotomic quiver Hecke superalgebras}},
  author = {Shuo Li and Lei Shi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29403},
  eprint = {2610.29403},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29403},
}
RIS
TY  - UNPB
TI  - Frobenius forms and semisimplicity of cyclotomic quiver Hecke superalgebras
AU  - Shuo Li
AU  - Lei Shi
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29403
UR  - https://arxiv.org/abs/2610.29403
AB  - We determine the Nakayama automorphism of the canonical homogeneous Frobenius form on cyclotomic quiver Hecke superalgebras. We give explicit necessary and sufficient conditions on the dominant weight and the rank for semisimplicity of cyclotomic quiver Hecke superalgebras of types A_e^(1), C_e^(1), A_2e^(2), D_e+1^(2), A_∞, B_∞, and C_∞. As an application, we prove that a cyclotomic Hecke--Clifford superalgebra is semisimple if and only if the corresponding Poincaré polynomial is nonzero.
ER  -