# Daniel Orr

dorr@vt.edu

Associate Professor

Department of Mathematics

Virginia Tech

Office | |
530 McBryde Hall |

Phone | |
(540) 231-6510 |

Fax | |
(540) 231-5960 |

Address | |
Mathematics (MC 0123)
McBryde, RM 460
Virginia Tech
225 Stanger Street
Blacksburg, VA 24061 |

### Research

My research lies in representation theory and algebraic combinatorics. I am interested primarily in structures related to Hecke algebras and Macdonald polynomials.

#### Preprints

- Daniel Orr

*Equivariant **K*-theory of the semi-infinite flag manifold as a nil-DAHA module

arXiv

- Daniel Orr and Mark Shimozono

*On cyclic quiver parabolic Kostka-Shoji polynomials*

arXiv

- Daniel Orr and Mark Shimozono

*Quiver Hall-Littlewood functions and Kostka-Shoji polynomials*

arXiv

#### Publications

- Takafumi Kouno, Satoshi Naito, Daniel Orr, and Daisuke Sagaki

*Inverse **K*-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type

Advances in Mathematics, to appear.

arXiv

- Satoshi Naito, Daniel Orr, and Daisuke Sagaki

*Chevalley formula for anti-dominant weights in the equivariant K-theory of semi-infinite flag manifolds*

Forum of Mathematics, Sigma, to appear.

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, Amer. Math. Soc., 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

#### Talk slides, etc.

Slides and

video
from a talk ''Specializations of nonsymmetric Macdonald polynomials at infinity''
at the workshop

Whittaker Functions: Number Theory, Geometry, and Physics, Banff International Research Station (October 2013).