The dimension formula for certain twisted Jacquet modules of a cuspidal representation of GL(n,Fq)
Let n≥2 be a positive integer. Let F be the finite field of order q and G=GL(n,F). Let P=MN be the standard parabolic subgroup of G corresponding to the partition (k,n−k). Let A∈M((n−k)×k,F) be a rank t matrix. In this paper, we compute the dimension formula for the twisted Jacquet module πN,ψA that...
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| Vydáno v: | Linear algebra and its applications Ročník 710; s. 151 - 164 |
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01.04.2025
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| Abstract | Let n≥2 be a positive integer. Let F be the finite field of order q and G=GL(n,F). Let P=MN be the standard parabolic subgroup of G corresponding to the partition (k,n−k). Let A∈M((n−k)×k,F) be a rank t matrix. In this paper, we compute the dimension formula for the twisted Jacquet module πN,ψA that depends on n,k and t, when π is an irreducible cuspidal representation of G and ψA is a character of N associated with A. |
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| AbstractList | Let n≥2 be a positive integer. Let F be the finite field of order q and G=GL(n,F). Let P=MN be the standard parabolic subgroup of G corresponding to the partition (k,n−k). Let A∈M((n−k)×k,F) be a rank t matrix. In this paper, we compute the dimension formula for the twisted Jacquet module πN,ψA that depends on n,k and t, when π is an irreducible cuspidal representation of G and ψA is a character of N associated with A. |
| Author | Balasubramanian, Kumar Khurana, Himanshi |
| Author_xml | – sequence: 1 givenname: Kumar surname: Balasubramanian fullname: Balasubramanian, Kumar email: bkumar@iiserb.ac.in organization: Department of Mathematics, IISER Bhopal, Bhopal, Madhya Pradesh 462066, India – sequence: 2 givenname: Himanshi surname: Khurana fullname: Khurana, Himanshi email: himanshikhurana@hri.res.in organization: Department of Mathematics, Harish-Chandra Research Institute, a CI of Homi Bhabha National Institute, Prayagraj, Uttar Pradesh 211019, India |
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| Cites_doi | 10.1155/S1073792800000313 10.1016/j.jpaa.2021.106932 10.1016/j.jnt.2024.12.006 10.1007/s00209-018-2097-y 10.1016/j.laa.2024.10.011 10.1090/S0002-9947-1955-0072878-2 10.1016/j.jpaa.2024.107614 |
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| References | Prasad (br0110) 2000 Steinberg, Faulkner, Wilson (br0120) 1967 Balasubramanian, Dangodara, Khurana (br0010) 2025 Gel'fand, Graev (br0070) 1962; vol. 147 Balasubramanian, Khurana (br0040) 2024; 228 Gorodetsky, Hazan (br0080) 2019; 291 Green (br0090) 1955; 80 Kawanaka (br0100) 1985; vol. 6 Balasubramanian, Kaipa, Khurana (br0020) 2025; 704 Balasubramanian, Khurana (br0030) 2022; 226 Bhatnagar (br0050) 2011; 18 Gasper, Rahman (br0060) 2004 Balasubramanian (10.1016/j.laa.2025.01.027_br0040) 2024; 228 Balasubramanian (10.1016/j.laa.2025.01.027_br0020) 2025; 704 Balasubramanian (10.1016/j.laa.2025.01.027_br0010) 2025 Green (10.1016/j.laa.2025.01.027_br0090) 1955; 80 Bhatnagar (10.1016/j.laa.2025.01.027_br0050) 2011; 18 Gel'fand (10.1016/j.laa.2025.01.027_br0070) 1962; vol. 147 Gasper (10.1016/j.laa.2025.01.027_br0060) 2004 Balasubramanian (10.1016/j.laa.2025.01.027_br0030) 2022; 226 Kawanaka (10.1016/j.laa.2025.01.027_br0100) 1985; vol. 6 Gorodetsky (10.1016/j.laa.2025.01.027_br0080) 2019; 291 Prasad (10.1016/j.laa.2025.01.027_br0110) 2000 Steinberg (10.1016/j.laa.2025.01.027_br0120) 1967 |
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| Title | The dimension formula for certain twisted Jacquet modules of a cuspidal representation of GL(n,Fq) |
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