Representation theory and algebraic geometry.
D. Muthiah and D. Orr, "On the double-affine Bruhat order: the $\varepsilon=1$ conjecture and classification of covers in ADE type." [arXiv:1609.03653] (To appear in Algebr. Comb. )
D. Muthiah and P. Tingley, "Affine PBW Bases and Affine MV polytopes."
Selecta Math. (N.S.) (2018). https://doi.org/10.1007/s00029-018-0436-9
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:1611.06775]
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.
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.
D. Muthiah, 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).
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. 1-23. doi:10.1017/S1474748017000214 [arXiv:1602.06451]
D. Muthiah and P. Tingley, "Affine PBW Bases and MV Polytopes in Rank 2." Selecta Math. (N.S.) 20 (2014), no. 1, 237--260.
D. Muthiah, "Double MV cycles and the Naito-Sagaki-Saito crystal." Adv. Math. 240 (2013), 268 - 290.
D. Muthiah, "Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities." [Link]
D. Muthiah, A. Puskás, and I. Whitehead, "Correction factors for Kac-Moody groups and t-deformed root multiplicities." [arXiv:1806.05209] (Submitted)
D. Muthiah, A. Weekes, and O. Yacobi, "The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman." [arXiv:1708.06076] (Submitted)