A Remark on Kirillov Model of GL(n)

Abstract

In this note, we derive another kernel formula for Bessel functions attached to supercuspidal representations of GL_n(F) over p-adic fields, and obtain another Kirillov model as a corollary.

Keywords

Kirillov model / kernel formula / Bessel function / 22E50 / 20C33

References

[1] BaruchEM. On Bessel distributions of GL(2) over a p-adic field. J. Number Theory, 1997, 67(2): 190-202.

[2] BaruchEM. Bessel distribution for GL(3) over the p-adics. Pacific J. Math., 2004, 217(1): 11-27.

[3] BaruchEMBessel functions for GL(n) over a p-adic field, 2005, Berlin. Walter de Gruyter. 14011

[4] BaruchEM, MaoZ. Bessel identities in the Waldspurger correspondence over a p-adic field. Amer. J. Math., 2003, 125(2): 225-288.

[5] ChaiJ. A weak kernel formula for Bessel functions. Trans. Amer. Math. Soc., 2017, 369(10): 7139-7167.

[6] ChaiJ. Bessel functions and local converse conjecture of Jacquet. J. Eur. Math. Soc. (JEMS), 2019, 21(6): 1703-1728.

[7] Gel’fandIM, KajdanD. Representations of the group GL(n, K) where K is a local field. Lie Groups and Their Representations (Proc. Summer School, Bolyai Janos Math. Soc., Budapest, 1971), 1975, New York. Halsted Press. 95118

[8] JacquetH. On the nonvanishing of some L-functions. Proc. Indian Acad. Sci. Math. Sci., 1987, 97(1–3): 117-155.

[9] LapidE, MaoZ. Stability of certain oscillatory integrals. Int. Math. Res. Not. IMRN, 2013, 2013(3): 525-547.

[10] Miao X., Bessel functions and Kloosterman integrals on GL(n). J. Funct. Anal., 2024, 286(4): Paper No. 110267, 62 pp.

[11] WaldspurgerJ-L. Correspondence de Shimura. J. Math. Pures Appl. (9), 1980, 59(1): 1-132

RIGHTS & PERMISSIONS

Peking University

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.