1,316 research outputs found
On Factorization of Generalized Macdonald Polynomials
A remarkable feature of Schur functions -- the common eigenfunctions of
cut-and-join operators from -- is that they factorize at the
peculiar two-parametric topological locus in the space of time-variables, what
is known as the hook formula for quantum dimensions of representations of
and plays a big role in various applications. This factorization
survives at the level of Macdonald polynomials. We look for its further
generalization to {\it generalized} Macdonald polynomials (GMP), associated in
the same way with the toroidal Ding-Iohara-Miki algebras, which play the
central role in modern studies in Seiberg-Witten-Nekrasov theory. In the
simplest case of the first-coproduct eigenfunctions, where GMP depend on just
two sets of time-variables, we discover a weak factorization -- on a
codimension-one slice of the topological locus, what is already a very
non-trivial property, calling for proof and better understanding.Comment: 8 page
The 2-leg vertex in K-theoretic DT theory
K-theoretic Donaldson-Thomas counts of curves in toric and many related
threefolds can be computed in terms of a certain canonical 3-valent tensor, the
K-theoretic equivariant vertex. In this paper we derive a formula for the
vertex in the case when two out of three entries are nontrivial. We also
discuss some applications of this result.Comment: 27 page
Multivalued current-phase relationship in a.c. Josephson effect for a three-dimensional Weyl semimetal WTe
We experimentally study electron transport between two superconducting indium
leads, coupled to a single WTe crystal, which is a three-dimensional Weyl
semimetal. We demonstrate Josephson current in long 5~m In-WTe-In
junctions, as confirmed by the observation of integer (1,2,3) and fractional
(1/3, 1/2, 2/3) Shapiro steps under microwave irradiation. Demonstration of
fractional a.c. Josephson effect indicates multivalued character of the
current-phase relationship, which we connect with Weyl topological surface
states contribution to Josephson current. In contrast to topological insulators
and Dirac semimetals, we do not observe periodicity in a.c. Josephson
effect for WTe at different frequencies and power, which might reflect
chiral character of the Fermi arc surface states in Weyl semimetal.Comment: the text is seriously corrected. arXiv admin note: text overlap with
arXiv:1801.0955
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