Research Interests

Representation theory and algebraic geometry.

Papers

1. D. Muthiah and A. Puskás, "Pursuing Coxeter theory for Kac-Moody affine Hecke algebras." Selecta Math. (N.S.) 32 (2026), no. 1, 18. [arXiv] [journal]
2. D. Muthiah and A. Weekes, "Fundamental monopole operators and embeddings of Kac-Moody affine Grassmannian slices." Int. Math. Res. Not. IMRN 2024, no. 15, 11159–11189. [arXiv] [journal]
3. D. Muthiah and A. Weekes, "Symplectic leaves for generalized affine Grassmannian slices." Ann. Sci. Éc. Norm. Supér. 56 (2023), no. 1, 287–298. [arXiv] [journal]
4. D. Muthiah, A. Weekes, and O. Yacobi, "The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman." Int. Math. Res. Not. IMRN 2022, no. 3, 1922–1972. [arXiv] [journal]
5. D. Muthiah, "Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities." Adv. Math. 385 (2021), 107793. [arXiv] [journal]
6. D. Muthiah, A. Weekes, and O. Yacobi, "On a conjecture of Pappas and Rapoport about the standard local model for $GL_d$." J. Reine Angew. Math. 772 (2021), 175–185. [arXiv] [journal]
7. D. Muthiah, A. Puskás, and I. Whitehead, "Correction factors for Kac-Moody groups and $t$-deformed root multiplicities." Math. Z. 296 (2020), 127–145. [arXiv] [journal]
8. D. Muthiah and D. Orr, "On the double-affine Bruhat order: the $\varepsilon=1$ conjecture and classification of covers in ADE type." Algebr. Comb. 2 (2019), no. 2, 197–216. [arXiv] [journal]
9. D. Muthiah and P. Tingley, "Affine PBW Bases and Affine MV polytopes." Selecta Math. (N.S.) 24 (2018), no. 5, 4781–4810. [arXiv] [journal]
10. D. Muthiah, "On Iwahori-Hecke Algebras for $p$-adic Loop Groups: Double Coset Basis and Bruhat Order." Amer. J. Math. 140 (2018), no. 1, 221–244. [arXiv] [journal]
11. J. Kamnitzer, D. Muthiah, A. Weekes, and O. Yacobi, "Reducedness of affine Grassmannian slices in type A." Proc. Amer. Math. Soc. 146 (2018), no. 2, 861–874. [arXiv] [journal]
12. J. Kamnitzer, D. Muthiah, and A. Weekes, "On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian." Transform. Groups 23 (2018), no. 3, 707–722. [arXiv] [journal]
13. D. Muthiah and D. Orr, "Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties." Representations of Lie algebras, quantum groups and related topics, 187–203, Contemp. Math., 713 (2018). [arXiv] [book]
14. K.-H. Lee, C. Lenart, and D. Liu, with appendix by D. Muthiah and A. Puskás, "Whittaker functions and Demazure characters." J. Inst. Math. Jussieu (2018), 1–23. [arXiv] [journal]
15. D. Muthiah and P. Tingley, "Affine PBW Bases and MV Polytopes in Rank 2." Selecta Math. (N.S.) 20 (2014), no. 1, 237–260. [arXiv] [journal]
16. D. Muthiah, "Double MV cycles and the Naito-Sagaki-Saito crystal." Adv. Math. 240 (2013), 268–290. [arXiv] [journal]

Preprints

1. A. Hébert and D. Muthiah, "Completed Iwahori-Hecke algebra for Kac-Moody groups over local fields." [arXiv]
2. D. Muthiah, "Double affine Kazhdan-Lusztig polynomials via masures." [arXiv]