Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 15 min ago
PreprintCC BY-NC-SA 4.0arXiv

Trilinear Forms for GL2(𝔽q) via conjugacy classes

  • Ankita Parashar
  • Shiv Prakash Patel
Open at sourcePDFDOICite

Abstract

It is well known that for a finite group G, the number of elements in Irr(G) the set of irreducible representations up to isomorphism is the same as the number of elements in Conj(G) the set of conjugacy classes in G although there is no natural bijection between these two sets. For G=GL2(𝔽q), where 𝔽q is the finite field with q elements, we give a bijection between Irr(G) and Conj(G), which behaves well with the tensor product of irreducible representations on one side and the product of conjugacy classes on the other. In particular, we relate the dimension of the trilinear forms with the multiplicity of the identity element in the triple product of the corresponding conjugacy classes.

Related

  1. On the number of ℓ-regular conjugacy classes
    Zhicheng Feng
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. The flag major index on conjugacy classes of wreath products
    Harel Rozenfeld
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  3. Categorical and Floer-theoretic entropies: comparison and counting conjugacy classes in symplectic mapping class groups
    Sangjin Lee
    arXivPreprintarXiv licenceFull textDynamical systemsGeometry & topologyarXiv
  4. On the order of a finite group with trivial centre and bounded conjugacy classes
    Ilya Gorshkov
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Finite groups with conjugacy classes of size 2pn
    Antonio Beltran, Changguo shao
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{parashar2026trilinear,
  title = {{Trilinear Forms for $\rm GL_2(\mathbbF_q)$ via conjugacy classes}},
  author = {Ankita Parashar and Shiv Prakash Patel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23450},
  eprint = {2610.23450},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23450},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Trilinear Forms for GL_2(𝔽_q) via conjugacy classes
AU  - Ankita Parashar
AU  - Shiv Prakash Patel
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23450
UR  - https://arxiv.org/abs/2610.23450
AB  - It is well known that for a finite group G, the number of elements in Irr(G) the set of irreducible representations up to isomorphism is the same as the number of elements in Conj(G) the set of conjugacy classes in G although there is no natural bijection between these two sets. For G=GL_2(𝔽_q), where 𝔽_q is the finite field with q elements, we give a bijection between Irr(G) and Conj(G), which behaves well with the tensor product of irreducible representations on one side and the product of conjugacy classes on the other. In particular, we relate the dimension of the trilinear forms with the multiplicity of the identity element in the triple product of the corresponding conjugacy classes.
ER  -