Daniel Orr

Associate Professor
Department of Mathematics
Virginia Tech

530 McBryde Hall

dorr@math.vt.edu

CV

Google Scholar

Research

Preprints

• Kamyar Amini, Irit Huq-Kuruvilla, Leonardo C. Mihalcea, Daniel Orr, and Weihong Xu
  Toda-type presentations for the quantum K theory of partial flag varieties
  arXiv


• Milo Bechtloff Weising and Daniel Orr
  Stable-limit partially symmetric Macdonald functions and parabolic flag Hilbert schemes
  arXiv


• Ben Goodberry and Daniel Orr
  A geometric realization of partially-symmetric Macdonald polynomials
  arXiv

Publications

• Daniel Orr, Mark Shimozono, and Joshua Jeishing Wen
  Wreath Macdonald operators
  Forum of Mathematics, Sigma, to appear (2025).
  arXiv


• Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi, and Daniel Orr
  Peter-Weyl theorem for Iwahori groups and highest weight categories
  Transformation Groups, to appear (2025).
  arXiv


• Evgeny Feigin, Ievgen Makedonskyi, and Daniel Orr
  Nonsymmetric q-Cauchy identity and representations of the Iwahori algebra
  Kyoto Journal of Mathematics, to appear (2025).
  arXiv


• Daniel Orr and Mark Shimozono
  Wreath Macdonald polynomials, a survey
  A glimpse into geometric representation theory, 123-169, Contemporary Mathematics, 804, American Mathematical Society, Providence, RI, 2024.
  volume arXiv


• Daniel Orr and Mark Shimozono
  Difference operators for wreath Macdonald polynomials
  Categorical, combinatorial and geometric representation theory and related topics, 483-492. Proceedings of Symposia in Pure Mathematics, 108, American Mathematical Society, Providence, RI, 2024.
  volume arXiv


• Takafumi Kouno, Satoshi Naito, and Daniel Orr
  Identities of inverse Chevalley type for graded characters of level-zero Demazure submodules over quantum affine algebras of type C
  Algebras and Representation Theory 27 (2024), no. 1, 429-460.
  journal arXiv


• Daniel Orr
  Equivariant K-theory of the semi-infinite flag manifold as a nil-DAHA module
  Selecta Mathematica (N.S.) 29 (2023), no. 3, Paper No. 45, 26 pp.
  journal arXiv


• Cristian Lenart, Satoshi Naito, Daniel Orr, and Daisuke Sagaki
  Inverse K-Chevalley formulas for semi-infinite flag manifolds, II: arbitrary weights in ADE type
  Advances in Mathematics 423 (2023), Paper No. 109037, 63 pp.
  journal arXiv


• Daniel Orr, Mark Shimozono, and Joshua Jeishing Wen
  Wreath Macdonald operators (extended abstract)
  Séminaire Lotharingien de Combinatoire 89B (2023), Art. 51, 12 pp.
  journal arXiv


• Daniel Orr and Mark Shimozono
  Quiver Hall-Littlewood functions and Kostka-Shoji polynomials
  Pacific Journal of Mathematics 319 (2022), no. 2, 397-437.
  journal arXiv


• Daniel Orr and Mark Shimozono
  On cyclic quiver parabolic Kostka-Shoji polynomials
  Journal of Combinatorial Theory, Series A 190 (2022), Paper No. 105634.
  journal arXiv


• Takafumi Kouno, Satoshi Naito, Daniel Orr, and Daisuke Sagaki
  Inverse K-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
  Forum of Mathematics Sigma 9 (2021), Paper No. e51, 25 pp.
  journal arXiv


• Satoshi Naito, Daniel Orr, and Daisuke Sagaki
  Chevalley formula for anti-dominant weights in the equivariant K-theory of semi-infinite flag manifolds
  Advances in Mathematics 387 (2021), Paper No. 107828, 59 pp.
  journal arXiv


• Dinakar Muthiah and Daniel Orr
  On the double-affine Bruhat order: the ε = 1 conjecture and classification of covers in ADE type
  Algebraic Combinatorics 2 (2019), no. 2, 197-216.
  journal arXiv


• Evgeny Feigin, Ievgen Makedonskyi, and Daniel Orr
  Generalized Weyl modules and nonsymmetric q-Whittaker functions
  Advances in Mathematics 330 (2018), 997-1033.
  journal arXiv


• Dinakar Muthiah and Daniel Orr
  Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties
  Representations of Lie algebras, quantum groups and related topics, 187-203, Contemporary Mathematics, 713, American Mathematical Society, Providence, RI, 2018.
  volume arXiv


• Daniel Orr and Mark Shimozono
  Specializations of nonsymmetric Macdonald-Koornwinder polynomials
  Journal of Algebraic Combinatorics 47 (2018), no. 1, 91-127.
  journal arXiv


• Daniel Orr and Leonid Petrov
  Stochastic higher spin six vertex model and q-TASEPs
  Advances in Mathematics 317 (2017), 473-525.
  journal arXiv


• Ivan Cherednik and Daniel Orr
  Nonsymmetric difference Whittaker functions
  Mathematische Zeitschrift 279 (2015), no. 3-4, 879-938.
  journal arXiv


• Ivan Cherednik and Daniel Orr
  One-dimensional nil-DAHA and Whittaker functions II
  Transformation Groups 18 (2013), no. 1, 23-59.
  journal arXiv


• Ivan Cherednik and Daniel Orr
  One-dimensional nil-DAHA and Whittaker functions I
  Transformation Groups 17 (2012), no. 4, 953-987.
  journal arXiv

Editorial

• AMS Special Session-Macdonald Theory and Beyond: Combinatorics, Geometry, and Integrable Systems, edited by Daniel Orr and Joshua Wen
  Contemporary Mathematics, 815, American Mathematical Society, Providence, RI, 2025. vii+159 pp.
  volume

Ph.D. Students

• Johnny Rivera, Jr. (current)
• Richard Shaplin
• Ben Goodberry
• Amanda Welch