ON SOME RELATIVELY CUSPIDAL REPRESENTATIONS : CASES OF GALOIS AND INNER INVOLUTIONS ON GLn

[1] E. Bannai and H. Tanaka: The decomposition of the permutation character 1GL(2n,q), J. Algebra 265 (2003), 496–512.

[2] I.N. Bernstein and A.V. Zelevinsky: Induced representations of p-adic groups I, Ann. Sci. Ec. Norm. Sup. 10 (1977), 441–472.

[3] Y. Flicker: On distinguished representations, J. reine angew. Math. 418 (1991), 139–172.

[4] I.M. Gel’fand and D. Kazhdan: Representations of the group GL(n, K) where K is a local field; in Lie Groups and their Representations, John Wiley and Sons, New York, 1975, 95–118.

[5] J. Guo: Uniqueness of generalized Waldspurger model for GL(2n), Pacific J. Math. 180 (1997), 273–289.

[6] J. Hakim and Z. Mao: Supercuspidal representations of GL(n) distinguished by a unitary subgroup, Pacific J. Math. 185 (1998), 149–162.

[7] J. Hakim and F. Murnaghan: Two types of distinguished supercuspidal representations, Int. Math. Res. Notices 35 (2002), 1857–1889.

[8] J. Hakim and F. Murnaghan: Distinguished tame supercuspidal representations, Int. Math. Res. Papers, 2008.

[9] A.G. Helminck and S.P. Wang: On rationality properties of involutions of reductive groups, Adv. Math. 99 (1993), 26–96.

[10] A. Henderson: Symmetric subgroup invariants in irreducible representations of GF , when G = GLn, J. Algebra 261 (2003), 102–144.

[11] H. Jacquet and S. Rallis: Uniqueness of linear periods, Compositio Math. 102 (1996), 65–123.

[12] D. Jiang, C. Nien and Y. Qin: Local Shalika models and functoriality, Manuscripta Math. 127 (2008), 187–217.

[13] S. Kato and K. Takano: Subrepresentation theorem for p-adic symmetric spaces, Int. Math. Res. Notices 2008(12) (2008), 1–40.

[14] E. Lapid and Z. Mao: Whittaker-Fourier coeflcients of cusp forms on Spn: reduction to a local statement, Amer. J. Math. 139 (2017), 1–55.

[15] N. Matringe: Cuspidal representations of GL(n, F) distinguished by a maximal Levi subgroup, with F a non-archimedean local field, C. R. Acad. Sci. Paris, Ser.I 350 (2012), 797–800.

[16] N. Matringe: Linear and Shalika local periods for the mirabolic group, and some consequences, J. Number Theory 138 (2014), 1–19.

[17] F. Murnaghan: Distinguished positive regular representations, Bull. Iranian Math. Soc. 43 (2017), 291– 311.

[18] O. Offen: On local root numbers and distinction, J. reine angew. Math 652 (2011) 165–205.

[19] O. Offen: On parabolic induction associated with a p-adic symmetric space, J. Number Theory 170 (2017) 211–227.

[20] J.M. Smith: Relative discrete series representations for two quotients of p-adic GLn, Canad. J. Mathematics 70 (2018), 1339–1372.

[21] A.V. Zelevinsky: Induced representations of p-adic groups II, Ann. Sci. Ec. Norm. Sup. 13 (1980), 165– 210.