Daniel L. Orr
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View article: Inflammatory Molecule Elaboration in Secondhand Smoke (SHS)-Induced or Conditional RAGE Transgenic Modeling of Chronic Rhinosinusitis (CRS)
Inflammatory Molecule Elaboration in Secondhand Smoke (SHS)-Induced or Conditional RAGE Transgenic Modeling of Chronic Rhinosinusitis (CRS) Open
Chronic rhinosinusitis (CRS) is characterized by sinonasal inflammation, mucus overproduction, and edematous mucosal tissue. This inflammatory condition is characterized by mucosal thickening, nasal obstruction, facial pain or pressure, hy…
View article: Combinatorial proof of a permuted basement Macdonald polynomial identity
Combinatorial proof of a permuted basement Macdonald polynomial identity Open
A well-known and fundamental property of the Macdonald polynomials $P_λ(x;q,t)$ is their invariance under the transformation sending $(q,t)$ to $(q^{-1},t^{-1})$. Recently, Concha and Lapointe showed that this property extends in an intere…
View article: Peter-Weyl Theorem for Iwahori Groups and Highest Weight Categories
Peter-Weyl Theorem for Iwahori Groups and Highest Weight Categories Open
We study the algebra of functions on the Iwahori group via the category of graded bounded representations of the Iwahori Lie algebra. In particular, we identify the standard and costandard objects in this category with certain generalized …
View article: Wreath Macdonald operators
Wreath Macdonald operators Open
We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald P -polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our …
View article: Stable-limit partially symmetric Macdonald functions and parabolic flag Hilbert schemes
Stable-limit partially symmetric Macdonald functions and parabolic flag Hilbert schemes Open
The modified Macdonald functions $\widetilde{H}_μ$ are fundamental objects in modern algebraic combinatorics. Haiman showed that there is a correspondence between the $(\mathbb{C}^{*})^2$-fixed points $I_μ$ of the Hilbert schemes $\mathrm{…
View article: A Geometric Realization of Partially-Symmetric Macdonald Polynomials
A Geometric Realization of Partially-Symmetric Macdonald Polynomials Open
We formulate a precise conjecture relating integral form partially-symmetric Macdonald polynomials and the parabolic flag Hilbert schemes of Carlsson, Gorsky, and Mellit. This extends, in an explicit fashion, Haiman's realization of modifi…
View article: Wreath Macdonald polynomials, a survey
Wreath Macdonald polynomials, a survey Open
Wreath Macdonald polynomials arise from the geometry of $Γ$-fixed loci of Hilbert schemes of points in the plane, where $Γ$ is a finite cyclic group of order $r\ge 1$. For $r=1$, they recover the classical (modified) Macdonald symmetric fu…
View article: Peter-Weyl theorem for Iwahori groups and highest weight categories
Peter-Weyl theorem for Iwahori groups and highest weight categories Open
We study the algebra of functions on the Iwahori group via the category of graded bounded representations of its Lie algebra. In particular, we identify the standard and costandard objects in this category with certain generalized Weyl mod…
View article: Equivariant K-theory of the semi-infinite flag manifold as a nil-DAHA module
Equivariant K-theory of the semi-infinite flag manifold as a nil-DAHA module Open
The equivariant K -theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions of the nil-double affine Hecke algebra (nil-DAHA) and a q -Heisenberg algebra. The action of the latt…
View article: Nonsymmetric $q$-Cauchy identity and representations of the Iwahori algebra
Nonsymmetric $q$-Cauchy identity and representations of the Iwahori algebra Open
The $t=0$ specialization of the Mimachi-Noumi Cauchy-type identity rewrites certain infinite product in terms of specialized nonsymmetric Macdonald polynomials of type $GL_n$. We interpret the infinite product as a character of the space o…
View article: Wreath Macdonald operators
Wreath Macdonald operators Open
We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald $P$-polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our…
View article: Identities of inverse Chevalley type for graded characters of level-zero Demazure submodules over quantum affine algebras of type C
Identities of inverse Chevalley type for graded characters of level-zero Demazure submodules over quantum affine algebras of type C Open
We provide identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules of extremal weight modules over a quantum affine algebra of type $C$. These identities express the product $e^μ \, \mathrm{gch} \, …
View article: Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, II: arbitrary weights in ADE type
Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, II: arbitrary weights in ADE type Open
We continue the study, begun in [Kouno-Naito-Orr-Sagaki, 2021], of inverse Chevalley formulas for the equivariant $K$-group of semi-infinite flag manifolds. Using the language of alcove paths, we reformulate and extend our combinatorial in…
View article: Difference operators for wreath Macdonald polynomials
Difference operators for wreath Macdonald polynomials Open
We give explicit $q$-difference operators acting diagonally on wreath Macdonald $P$-polynomials in finitely many variables.
View article: One-dimensional nil-DAHA and Whittaker functions II
One-dimensional nil-DAHA and Whittaker functions II Open
This paper is devoted to the theory of nil-DAHA for the root system A1 and its applications to symmetric and non-symmetric (spinor) global q-Whittaker functions. These functions integrate the q-Toda eigenvalue problem and its Dunkl-type no…
View article: A Review of Current Literature of Interest to the Office-Based Anesthesiologist
A Review of Current Literature of Interest to the Office-Based Anesthesiologist Open
Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Share Icon Share Twitter LinkedIn Tools Icon Tools Get Permissions Cite Icon Cite Search Site Citation Mark A. Saxen, Daniel L. Orr; A Review of Current Lite…
View article: Inverse<i>K</i>-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Inverse<i>K</i>-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type Open
We prove an explicit inverse Chevalley formula in the equivariant K -theory of semi-infinite flag manifolds of simply laced type. By an ‘inverse Chevalley formula’ we mean a formula for the product of an equivariant scalar with a Schubert …
View article: Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, I:\n minuscule weights in ADE type
Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, I:\n minuscule weights in ADE type Open
We prove an explicit inverse Chevalley formula in the equivariant $K$-theory\nof semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley\nformula, we mean a formula for the product of an equivariant scalar with a\nSchube…
View article: Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type Open
We prove an explicit inverse Chevalley formula in the equivariant $K$-theory of semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley formula, we mean a formula for the product of an equivariant scalar with a Schubert …
View article: Equivariant $K$-theory of the semi-infinite flag manifold as a nil-DAHA module
Equivariant $K$-theory of the semi-infinite flag manifold as a nil-DAHA module Open
The equivariant $K$-theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions of the nil-double affine Hecke algebra (nil-DAHA) and a $q$-Heisenberg algebra. The action of the la…
View article: Nonsymmetric Difference Whittaker Functions and Double Affine Hecke Algebras
Nonsymmetric Difference Whittaker Functions and Double Affine Hecke Algebras Open
This dissertation is devoted to a new theory of nonsymmetric difference Whittaker functions and the corresponding Toda-Dunkl operators for arbitrary reduced irreducible root systems. The nonsymmetric Whittaker functions are obtained as lim…
View article: On cyclic quiver parabolic Kostka-Shoji polynomials
On cyclic quiver parabolic Kostka-Shoji polynomials Open
We obtain an explicit combinatorial formula for certain parabolic Kostka-Shoji polynomials associated with the cyclic quiver, generalizing results of Shoji and of Liu and Shoji.
View article: On the double-affine Bruhat order: the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ε</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> conjecture and classification of covers in ADE type
On the double-affine Bruhat order: the conjecture and classification of covers in ADE type Open
For any Kac–Moody group , we prove that the Bruhat order on the semidirect product of the Weyl group and the Tits cone for is strictly compatible with a -valued length function. We conjecture in general and prove for of affine ADE type t…
View article: Chevalley formula for anti-dominant weights in the equivariant $K$-theory of semi-infinite flag manifolds
Chevalley formula for anti-dominant weights in the equivariant $K$-theory of semi-infinite flag manifolds Open
We prove a Pieri-Chevalley formula for anti-dominant weights and also a Monk formula in the torus-equivariant $K$-group of the formal power series model of semi-infinite flag manifolds, both of which are described explicitly in terms of se…
View article: A Review of Current Literature of Interest to the Office-Based Anesthesiologist
A Review of Current Literature of Interest to the Office-Based Anesthesiologist Open
Cardiac arrest in the operating room and procedural areas has a spectrum of causes (eg, hypovolemia, gas embolism, and hyperkalemia) that are not directly reflected in the standard advanced cardiac life support (ACLS) recommendations. Rapi…
View article: Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties
Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties Open
We study walk algebras and Hecke algebras for Kac-Moody root systems. Each choice of orientation for the set of real roots gives rise to a corresponding "oriented" basis for each of these algebras. We show that the notion of distinguished …
View article: Quiver Hall-Littlewood functions and Kostka-Shoji polynomials
Quiver Hall-Littlewood functions and Kostka-Shoji polynomials Open
For any triple $(i,a,μ)$ consisting of a vertex $i$ in a quiver $Q$, a positive integer $a$, and a dominant $GL_a$-weight $μ$, we define a quiver current $H^{(i,a)}_μ$ acting on the tensor power $Λ^Q$ of symmetric functions over the vertic…