Santosh Nadimpalli
Assistant Professor
Department of Mathematics and Statistics
Indian Institute of Technology, Kanpur.
Office address: Mathematics department FB588.
Phone number: Add usual IITK with extension 2149.
Email: nsantosh 'at' iitk 'dot' ac 'dot' in
Research area: Representation theory.
A note for prospective students:
I am looking for Ph.D Students.
I am interested in representation theory of
p-adic reductive groups, finite groups of Lie type,
real reductive groups.
I like to think about problems motivated by
local
Langlands program, so problems usually involve
interactions between
number theory and representation theory.
I also work on algebraic
representations.
Publications/Preprints:
Typical representations for level zero Bernstein components of
${\rm GL}_n(F)$,
Journal of Algebra 2017, Volume 469 1-29.
On Classification of Typical representations for
${\rm GL}_3(F)$,
Forum Mathematicum 2019, Volume 31, 917-941.
On Extensions of supersingular representations for ${\rm
SL}_2(\mathbb{Q}_p)$,
Journal of Number theory 2019, volume 119.
On Typical representations for depth-zero Bernstein components of
split classical groups
with A. K. Mondal, Representation theory of AMS 2019, volume
23.
Generic cuspidal representations of ${\rm U}(2,1)$,
Forum Mathematicum, Volume 33, Issue 3, May 2021, 709-742.
On the uniqueness of branching to fixed
point Lie subalgebras
with S. Pattanayak, Forum Mathematicum,
Volume 34, Issue 6, November 2022, 1663-1678.
A note on Branching of $V(\rho)$
with S.Pattanayak, Journal of Algebra, Volume 594, 15 March 2022,
194-201
On the duality involution for General spin
groups
with A. K. Mondal, Journal of Number theory,
248(2023) 1-13.
Quotients of commuting schemes associated to symmetric
pairs
with S. Pattanayak. To appear in Transformation groups
Tate cohomology of Whittaker lattices in
cuspidal representations of GL_n
with Sabyasachi Dhar, International Mathematics Research Notices,
Volume 2024, Issue 19, 12761-12795.
On the integrality of locally algebraic representations
of GL(2,D)
With Mihir Sheth, Journal of Number theory, Volume 257, April
2024,124-145
Twisted Jacquet modules: A conjecture of
D. Prasad
with Mihir Sheth, To appear in Proceedings of AMS.
Families over the integral Bernstein centre and
Tate cohomology of local base change lifts
(With Sabyasachi Dhar)
This paper has a gap in the main theorem. We
hope to fix it soon. The problem is that the Frobenius morphism may kill
some nilpotents in the mod-$l$ Bernstein centre which is usually
non-reduced. So the induction step in the main theorem is not complete.
However, the proof must work for n=3 and also in the case where
l is non-abanal for n-1, we get a result in families.
Notes:
These are some notes and results which I wrote for fun
On mod-$l$ reduction of cuspidal
representations of ${\rm
GL}_2(F)$
Extensions of characters of pro-$p$-Iwahori
Hecke algebra.
On the $I(1)$-invariants of universal supersingular quotient
Current Student: Sabyasachi Dhar
Thesis topic: Tate cohomology and local Langlands correspondance.