Notes and Publications

 Preprints Accepted Published Supervised Others

Books
1. Representation Theory: A Combinatorial Viewpoint, Cambridge University Press, 2015.
Preprints
1. Schur algebras for the alternating group and Koszul duality, with Thangavelu Geetha and Shraddha Srivastava, 2019.
2. Macdonald trees and determinants of representations for finite Coxeter groups, with Arvind Ayyer and Steven Spallone, 2018.
3. A Timed Version of the Plactic Monoid, 2018.
4. An Introduction to Schur Polynomials, 2018.
5. Residues modulo powers of two in the Young-Fibonacci lattice, with N. Karimilla Bi and Giftson P. Santhosh, 2017.
6. Growth in Right-Angled Groups and Monoids, with Jayadev S. Athreya.
7. Equivalence Classes of Nodes in Trees and Rational Generating Functions.
Accepted
1. Tableau Correspondences and Representation Theory, with Digjoy Paul and Arghya Sadhukhan, To appear in the proceedings of the International Conference on Algebra, Discrete Mathematics and Applications.
Published
1. Knuth's moves on Timed Words. The Mathematics Student, published by the Indian Mathematical Society, 87,(3-4):1-11, 2018.
2. Comparison of Gelfand-Tsetlin Bases for Alternating and Symmetric Groups, with T. Geetha, Algebras and Representation theory, 21(1):131-143, 2018.
3. Representations of symmetric groups with non-trivial determinant, with Arvind Ayyer and Steven Spallone, J. Combin. Th., Ser. A, 150:208-232, 2017.
4. Odd Partitions in Young's lattice, with Arvind Ayyer and Steven Spallone, Sém. Lothar. Combin., vol. 75, art. B75g, 2016.
5. The Centre of the Schur algebra, with T. Geetha, Asian European J. Math., 9(1):165006, 2016.
6. On similarity of matrices over local rings of length two, with Pooja Singla and Steven Spallone, Indiana Univ. Math. J, 64(2):471-514, 2015.
7. Combinatorics of finite abelian groups and Weil representations, with Kunal Dutta, Pac. J. Math, 275(2):295-324, 2015.
8. Graphic Interpretation of the Structure Constants of the Schur Algebra, with T. Geetha, Electronic booklet of Proceedings of International Congress of Women Mathematicians (ICWM 2014). 2014 ICWM Poster Abstract Number: 20140020.
9. Orbits of pairs in Abelian groups, with C. P. Anilkumar, Sém. Lothar. Combin., vol. 70, article B70h (24 pages) 2014.
10. Degeneration and orbits of tuples and subgroups in an Abelian group, with Wesley Calvert and Kunal Dutta, J. Group Theory, 16:221-233, 2013.
11. Buildings, extensions, and volume growth entropy, with Jayadev Athreya and Anish Ghosh, New York J. Math., 19:1-11, 2013.
12. Ultrametric logarithm laws, II, with Jayadev S. Athreya and Anish Ghosh. Monatsh. Math., 167(3):333-356, 2012.
13. The Cartan matrix of a Centralizer algebra, with Umesh V. Dubey and Pooja Singla. Proc. Indian Acad. Sci. Math. Sci., 122(1):67-73, 2012.
14. An easy proof of the Stone-von Neumann-Mackey theorem. Exposition. Math., 24:110-118, 2011.
15. Degenerations and orbits in finite abelian groups, with Kunal Dutta. J. Combin. Theory Ser. A., 118:1685-1694, 2011.
16. Counting subspaces of a finite vector space. Resonance, 15:977-987;1074-1083, 2010.
17. Inductive algebras and homogeneous shifts, with M. K. Vemuri. Compl. Anal. Oper. Theory, 4:1015-1027, 2010.
18. Locally compact abelian groups with symplectic self-duality, with Ilya Shapiro and M. K. Vemuri. Adv. Math., 225:2429-2454, 2010.
19. Iwahori-Hecke Algebras, with Thomas J. Haines and Robert E. Kottwitz. J. Ramanujan Math. Soc., 25:113-145, 2010.
20. Inductive algebras for finite Heisenberg groups, with M. K. Vemuri. Comm. Algebra, 38:509-514, 2010.
21. On cuspidal representations of general linear groups over discrete valuation rings, with Anne-Marie Aubert, Uri Onn and Alexander Stasinski. Israel J. Math., 175:391-420, 2010.
22. On character values and decomposition of the Weil representation associated to a finite abelian group. J. Analysis, 17:73-86, 2009.
23. Similarity classes of 3x3 matrices over a local principal ideal ring, with Nir Avni, Uri Onn and Leonid Vaserstein. Comm. Algebra, 37:2601-2615, 2009.
24. Ultrametric logarithm laws I, with Jayadev Athreya and Anish Ghosh. Discrete Contin. Dynam. Syst. Ser. S, 2:337-348, 2009.
25. Eigenfunctions of the Laplace-Beltrami operator on hyperboloids, with M. K. Vemuri. Tamkang J. Math., 39:335-339, 2008.
26. Representations of a finite group in positive characteristic, Math. Newsl. Ramanujan Math. Soc., 16:73-78, 2007.
27. A note on Bruhat decomposition over local principal ideal rings, with Uri Onn and Leonid Vaserstein, Comm. Algebra, 34:4119--4130, 2006.
28. On Bernstein's presentation of Iwahori-Hecke algebras and representations of split reductive groups over non-Archimedean local fields, Bull. Kerala Math. Assoc. (special issue on harmonic analysis and quantum groups), December 2005.
29. Almost unramified automorphic representations for split groups over Fq(t), J. Algebra, 262:253--261, 2004.
30. Reduction theory for a rational function field, Proc. Indian Acad. Sci. Math. Sci. 113:153--163, 2003.
31. Almost unramified discrete spectrum for split groups over Fq(t), Duke Math. J., 113:237--257, 2002.
32. Almost unranified discrete spectrum for split semisimple groups over a rational function field, University of Chicago Ph.D. thesis, 2001.
Supervised work
1. Orbits of pairs in finite modules over discrete valuation rings and permutation representations, PhD thesis of C. P. Anilkumar, IMSc (2014), (download from IMSc library website).
2. Geometry of Linear Diophantine equations, MSc thesis of Kamalakshya Mahatab, IMSc (2012), (download from IMSc library website).
3. Representation Theory of Symmetric Groups, MSc thesis of Venkata Raghu Tej Pantangi, IISER Pune, (2012).
4. Representations and conjugacy classes of general linear groups over principal ideal local rings of length two, PhD thesis of Pooja Singla, IMSc (2010), (download from IMSc library website).
Notes, Slides, etc.
1. Automorphism orbits of subgroups in finite abelian groups, slides from a talk at ITCDM 2015 held at IIT Madras on 12 July 2015.
2. Matrices modulo $p^k$ and $k$ commuting matrices modulo $p$, slides from a talk at IISER Pune on 24 April 2015 ((beamer version).
3. Counting and Symmetry, slides from a talk on Polya theory given as part od DST INSPIRE Science camp on 14th October 2011 (pdf).
4. Representations of symmetric groups via the RSK correspondence, notes for a talk given at IISc on 23rd September 2011 (pdf).
5. Relative positions in finite abelian groups, slides from a talk given at the Institute Seminar Week 2011 (pdf).
6. Combinatorics of finite abelian groups and the Weil representation, slides from a talk given at the ICM satellite conference on Algebraic and Combinatorial Approaches to Representation Theory held at NIAS Bangalore in August 2010, and at the International Conference on Non-commutative Rings and Combinatorial Representation Theory held at Pondicherry University in September 2010 (pdf).
7. Faces of the Fourier transform, slides from a talk given at the workshop on Perspectives in Mathematics in Mumbai on December 21st, 2009 (pdf).
8. Mackey's little groups method (with M. K. Vemuri). (pdf).
9. Representations of GL2(Fq) and SL2(Fq) and some remarks about GLn(Fq) (Lecture notes from the Advanced Instructional School on Representation Theory and its Applications held in Pune in July 2007). (arXiv),(djvu),(html).
10. GL2(Fp) (notes from a course taught at the summer student programme in 2005). (pdf).