Minimal polynomials of the images of the unipotent elements of non-prime order in the irreducible representations of an algebraic group of type F4
https://doi.org/10.29235/1561-8323-2022-66-3-269-273
Abstract
The minimal polynomials of the images of the unipotent elements of non-prime order in the irreducible representations of an algebraic group of type F4 in characteristics 3 and 7 are found. This completes the solution of the minimal polynomial problem for unipotent elements in the irreducible representations of such a group in an odd characteristic.
About the Author
I. D. SuprunenkoBelarus
Suprunenko Irina D. – D. Sc. (Physics and Mathematics), Chief Researcher
References
1. Suprunenko I. D. Minimal polynomials of elements of order p in irreducible representations of Chevalley groups over fields of characteristic p. Siberian Advances in Mathematics, 1996, vol. 6, pp. 97–150.
2. Suprunenko I. D. The minimal polynomials of unipotent elements in irreducible representations of the classical groups in odd characteristic. Memoirs of the AMS, 2009, vol. 200, no. 939. https://doi.org/10.1090/memo/0939
3. Busel T. S., Suprunenko I. D., Testerman D. Minimal polynomials of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in some good characteristics. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2019, vol. 63, no. 5, pp. 519–525. https://doi.org/10.29235/1561-8323-2019-63-5-519-525
4. Hall P., Higman G. On the p-length of p-soluble groups and reduction theorem for Burnside’s problem. Proceedings of the London Mathematical Society, 1956, vol. s3-6, no. 1, pp. 1–42. https://doi.org/10.1112/plms/s3-6.1.1
5. Steinberg R. Lectures on Chevalley groups. Mimeographed lecture notes. Yale Univ. Math. Dept., New Haven, Conn., 1968.
6. Lawther R. Jordan block sizes of unipotent elements in exceptional algebraic groups. Communication in Algebra, 1995, vol. 23, no. 11, pp. 4125–4156. https://doi.org/10.1080/00927879508825454
7. Steinberg R. Representations of algebraic groups. Nagoya Mathematical Journal, 1963, vol. 22, pp. 33–56. https://doi.org/10.1017/s0027763000011016
8. Gudivok P. M., Rudko V. P. Tensor products of representations of finite groups. Uzhgorod, 1985 (in Russian).