Publications
79. Homological aspects of branching laws; based on my lecture at the IHES summer school in 2022, to appear.
78. (with WT Gan and BH Gross) Twisted GGP Problems and Conjectures. Compos. Math. 159 (2023), no. 9, 1916–1973..
77. Arithmetic in L-values, Indian Math Society's Presidential lecture (technical), Dec 2021,published in: The mathematics Student, vol 91, Nos 1-2, Janaury-June(2022), 9-28.
76. Mathematics in Post-independence India, Indian Math Society's Presidential lecture (general), published in: The mathematics Student, vol 91, Nos 1-2, Janaury-June(2022), 1-8.
75. (with Dragos Fratila) Homological duality for covering groups of reductive p-adic groups, Pure and Appl. Math. Q., a volume in honor of Benedict Gross, Volume 18, Number 5, 1867-1950 (2022).
74. A relative Langlands correspondence and Geometry of parameter spaces, still incomplete, but here is the latest version (2020).
73. (with R. Raghunathan) Relations between cusp forms sharing Hecke eigenvalues, arXiv:2007.14639 (2020). Electronic J. of the AMS, Representation Theory, Volume 26, Pages 1063–1079 (2022).
72. (with Arvind Nair) Cohomological representations for real reductive groups, J. Lond. Math. Soc. (2) 104 no. 4, 1515–1571 (2021).
71. (with F. Lubeck) A character relationship between symmetric group and hyperoctahedral group, J. Combin. Theory Ser. A 179 (2021), Paper No. 105368, 20 pp.
70. (with Vinay Wagh) Multiplicities for tensor products on Special linear versus Classical groups, Manuscripta Math. 167 (2022), no. 1-2, 65–87.
69. (with Sudhanshu Shekhar) Relating the Tate-Shafarevitch group of an elliptic curve with the classgroup; Pacific Journal, vol. 312, No. 1, 203-218 (2021).
68. (with W.T. Gan and B. Gross) Branching laws for classical groups: The non-tempered case. Compositio Math, vol 156, No. 11 (2020) 2298-2367.
67. (With M. Nori) On a duality theorem of Schneider-Stuhler. Crelle Journal 762 ,261-280 (2020).
66. Multiplicities under basechange: finite field case. J. Algebra 556, 1101–1114 (2020).
65. A mod-p Artin-Tate conjecture, and generalizing the Herbrand-Ribet theorem. Pacific J. Math. 303 (2019), no. 1, 299–316.
64. (with J. Adler) Multiplicity upon restriction to the derived subgroup. Pacific J. Math. 301 (2019), no. 1, 1–14.
63. Contributions to algebraic number theory from India: from independence to late 90's. Indian J. Pure Appl. Math. 50 (2019), no. 3, 779–793.
62. (with S. Dijols) Symplectic models for unitary groups. Trans. Amer. Math. Soc. 372 (2019), no. 3, 1833–1866.
61. Generalizing the MVW involution, and the contragredient. Trans. Amer. Math. Soc. 372 (2019), no. 1, 615–633.
60. Generic representations for symmetric spaces. With an appendix by Yiannis Sakellaridis. Adv. Math. 348 (2019), 378–411.
59. Ext-analogues of branching laws. Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. II. Invited lectures, 1367–1392, World Sci. Publ., Hackensack, NJ, 2018.
58. (with Anandavardhanan) Distinguished representations for SL(n). Math. Res. Lett. 25 (2018), no. 6, 1695–1717.
57. (with S.P. Patel) Restriction of representations of metaplectic GL2(F) to tori. Israel J. Math. 225 (2018), no. 2, 525–551.
56. (with J. Adams and G. Savin) Euler-Poincaré characteristic for the oscillator representation. Representation theory, number theory, and invariant theory, 1–22, Progr. Math., 323, Birkhäuser/Springer, Cham, 2017.
55. A refined notion of arithmetically equivalent number fields, and curves with isomorphic Jacobians. Adv. Math. 312 (2017), 198–208.
54. A character relationship on GLn(ℂ). Israel J. Math. 211 (2016), no. 1, 257–270.
53. Half the sum of positive roots, the Coxeter element, and a theorem of Kostant. Forum Math. 28 (2016), no. 1, 193–199.
52. (with S.P.Patel) Multiplicity formula for restriction of representations of GL2˜(F) to SL2˜(F).Proc. Amer. Math. Soc. 144 (2016), no. 2, 903–908.
51. (with S. Kumar) Dimension of zero weight space: an algebro-geometric approach. J. Algebra 403 (2014), 324–344.
50. (with Anandavardhanan) A local-global question in automorphic forms. Compos. Math. 149 (2013), no. 6, 959–995.
49. (with W.T.Gan and B. Gross) Restrictions of representations of classical groups: examples. Sur les conjectures de Gross et Prasad. I. Astérisque No. 346 (2012), 111–170.
48. (with W.T. Gan and B. Gross) Symplectic local root numbers, central critical L values, and restriction problems in the representation
theory of classical groups. Sur les conjectures de Gross et Prasad. I. Astérisque No. 346 (2012), 1–109.
47. (with J. Adler) Extensions of representations of p-adic groups. Nagoya Math. J. 208 (2012), 171–199.
46. (with D. Ramakrishnan) Self-dual representations of division algebras and Weil groups: a contrast. Amer. J. Math. 134 (2012), no. 3, 749–767.
45. (with Ramin Takloo-Bighash) Bessel models for GSp(4). J. Reine Angew. Math. 655 (2011), 189–243.
44. (with S. Kumar and G. Lusztig) Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups. Representation theory, 99–101, Contemp. Math., 478, Amer. Math. Soc., Providence, RI, 2009.
43. (with A. Raghuram) Representation theory of GL(n) over non-Archimedean local fields. School on Automorphic Forms on GL(n), 159–205, ICTP Lect. Notes, 21, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2008.
42. (with R. Schulze-Pillot) Generalised form of a conjecture of Jacquet and a local consequence. J. Reine Angew. Math. 616 (2008), 219–236.
41. Relating invariant linear form and local epsilon factors via global methods. With an appendix by Hiroshi Saito. Duke Math. J. 138 (2007), no. 2, 233–261.
40. (with Anandavardhanan) On the SL(2) period integral. Amer. J. Math. 128 (2006), no. 6, 1429–1453.
39. (with J. Adler)On certain multiplicity one theorems. Israel J. Math. 153 (2006), 221–245.
38. (with S.O. Juriaans and I.B.S. Passi) Hyperbolic unit groups. Proc. Amer. Math. Soc. 133 (2005), no. 2, 415–423.
37. An analogue of a conjecture of Mazur: a question in Diophantine approximation on tori. Contributions to automorphic forms, geometry, and number theory, 699–709, Johns Hopkins Univ. Press, Baltimore, MD, 2004.
36. (with C. Khare) Reduction of homomorphisms mod p and algebraicity. J. Number Theory 105 (2004), no. 2, 322–332.
35. (with Anandavardhanan) Distinguished representations for SL(2). Math. Res. Lett. 10 (2003), no. 5-6, 867–878.
34. The main theorem of complex multiplication. Elliptic curves, modular forms and cryptography (Allahabad, 2000), 109–118, Hindustan Book Agency, New Delhi, 2003.
33. (with C.S. Rajan) On an Archimedean analogue of Tate's conjecture. J. Number Theory 99 (2003), no. 1, 180–184.
32. (with N.Sanat) On the restriction of cuspidal representations to unipotent elements. Math. Proc. Cambridge Philos. Soc. 132 (2002), no. 1, 35–56.
31. The space of degenerate Whittaker models for GL(4) over p-adic fields. Cohomology of arithmetic groups, L-functions and automorphic forms (Mumbai, 1998/1999), 103–115, Tata Inst. Fund. Res. Stud. Math., 15, Tata Inst. Fund. Res., Bombay, 2001.
30. On a conjecture of Jacquet about distinguished representations of GL(n). Duke Math. J. 109 (2001), no. 1, 67–78.
29. (with P. Schneider and J. Teitelbaum) U(𝔤)-finite locally analytic representations. With an appendix by Dipendra Prasad.
Represent. Theory 5 (2001), 111–128.
28. (with C.S. Yogananda) Bounding the torsion in CM elliptic curves. C. R. Math. Acad. Sci. Soc. R. Can. 23 (2001), no. 1, 1–5.
27. (with C. Khare) On the Steinitz module and capitulation of ideals. Nagoya Math. J. 160 (2000), 1–15.
26. Comparison of germ expansion on inner forms of GL(n). Manuscripta Math. 102 (2000), no. 2, 263–268.
25. (with A. Raghuram) Kirillov theory for GL2(𝒟) where 𝒟 is a division algebra over a non-Archimedean local field. Duke Math. J. 104 (2000), no. 1, 19–44.
24. (with C.S. Yogananda) A report on Artin's holomorphy conjecture. Number theory, 301–314, Trends Math.,
Birkhäuser, Basel, 2000.
23. The space of degenerate Whittaker models for general linear groups over a finite field. Internat. Math. Res. Notices 2000, no. 11, 579–595.
22. Theta correspondence for unitary groups. Pacific J. Math. 194 (2000), no. 2, 427–438.
21. (with K. Murty) Tate cycles on a product of two Hilbert modular surfaces. J. Number Theory 80 (2000), no. 1, 25–43.
20. Distinguished representations for quadratic extensions. Compositio Math. 119 (1999), no. 3, 335–345.
19. (with D. Ramakrishnan) On the global root numbers of GL(n)×GL(m). Automorphic forms, automorphic representations, and arithmetic (Fort Worth, TX, 1996), 311–330, Proc. Sympos. Pure Math., 66, Part 2, Amer. Math. Soc., Providence, RI, 1999.
18. On the self-dual representations of a p-adic group. Internat. Math. Res. Notices 1999, no. 8, 443–452.
17. Some remarks on representations of a division algebra and of the Galois group of a local field. J. Number Theory 74 (1999), no. 1, 73–97.
16. On the self-dual representations of finite groups of Lie type. J. Algebra 210 (1998), no. 1, 298–310.
15. A brief survey on the theta correspondence. Number theory (Tiruchirapalli, 1996), 171–193, Contemp. Math., 210, Amer. Math. Soc., Providence, RI, 1998.
14. (with C. Khare) Extending local representations to global representations. J. Math. Kyoto Univ. 36 (1996), no. 3,
471–480.
13. Some applications of seesaw duality to branching laws. Math. Ann. 304 (1996), no. 1, 1–20.
12. (with D. Ramakrishnan) Lifting orthogonal representations to spin groups and local root numbers. Proc. Indian Acad. Sci. Math. Sci. 105 (1995), no. 3, 259–267.
11. Ribet's theorem: Shimura-Taniyama-Weil implies Fermat. Seminar on Fermat's Last Theorem (Toronto, ON, 1993–1994), 155–177, CMS Conf. Proc., 17, Amer. Math. Soc., Providence, RI, 1995.
10. On an extension of a theorem of Tunnell. Compositio Math. 94 (1994), no. 1, 19–28.
9. (with B. Gross) On irreducible representations of SO2n+1×SO2m. Canad. J. Math. 46 (1994), no. 5, 930–950.
8. Bézout's theorem for abelian varieties. Exposition. Math. 11 (1993), no. 5, 4
7. On the local Howe duality correspondence. Internat. Math. Res. Notices 1993, no. 11, 279–287.
6. Weil representation, Howe duality, and the theta correspondence. Theta functions: from the classical to the modern, 105–127, CRM Proc. Lecture Notes, 1, Amer. Math. Soc., Providence, RI, 1993.
4. Invariant forms for representations of GL2 over a local field. Amer. J. Math. 114 (1992), no. 6, 1317–1363.
3. (with B. Gross) On the decomposition of a representation of SOn when restricted to SOn−1. Canad. J. Math. 44 (1992), no. 5, 974–1002.
2. (with B. Gross) Test vectors for linear forms. Math. Ann. 291 (1991), no. 2, 343–355.
Trilinear forms for representations of GL(2) and local ϵ-factors. Compositio Math. 75 (1990), no. 1, 1–46.