Abstract We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type 4 0$, for which we obtain ...

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU (N ) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality...

We give a simple general extension to all free bosonic and fermionic massless gauge fields of a recent proof that spin 2 is duality invariant in flat space. We also discuss its validity in (A)dS backgrounds and the relevance of supersymmetry. Recently [1], it was shown that the duality invariance originally established [2] for Maxwell theory in D=4, extends to free massless spin 2. It was also ...

Generalizing the characters of compact simple Lie groups, Ian Macdonald introduced in [M1,M2] and other works remarkable orthogonal symmetric polynomials dependent on the parameters q, t. He came up with three main conjectures formulated for arbitrary root systems. A new approach to the Macdonald theory was suggested in [C1] on the basis of (double) affine Hecke algebras and related difference ...

Generalizing the characters of compact simple Lie groups, Ian Macdonald introduced in [M1,M2] and other works remarkable symmetric trigonometric polynomials dependent on the parameters q, t. He came up with four main conjectures formulated for arbitrary root systems. A new approach to the Macdonald theory was suggested in [C1] on the basis of double affine Hecke algebras (new objects in mathema...

We introduce a new algebra Bl(z, q) depending on two nonzero complex parameters such that Bl(q n , q) at q = 1 coincides with the Brauer algebra Bl(n). We establish an analog of the Brauer–Schur–Weyl duality where the action of the new algebra commutes with the representation of the twisted deformation Uq(on) of the enveloping algebra U(on) in the tensor power of the vector representation.

A representation of the quantum toroidal algebra of type sl N is de ned on every integrable irreducible highest weight module of the the quantum a ne algebra of type gl N : The q-version of the level-rank duality giving the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U 0 q ( b gl N ) of level L and U 0 q ( b sl L ) of level N is described.

The four constraints on sentential anaphoric binding, known as binding principles, are observed to form a square of oppositions. With the formal tools of phase quantification, these constraints are analysed as the effect of phase quantifiers over reference markers in grammatical obliqueness hierarchies. The four quantifiers are shown to be organized in a square of duality. The impact of this re...

We compare the cohomology ring of flag variety ${\\mathcal{F}\\ell}n$ and Chow Gelfand–Zetlin toric $X{\\operatorname{GZ}}$.We show that $H^(\\mathcal{F}{\\ell}\_n, \\mathbb{Q})$ is Poincaré duality quotient subalgebra $A^(X\_{\\operatorname{GZ}}, generated by degree $1$ elements. compute these algebras for $n=3$ see that, in general, this does not have duality.