Julien Roussillon
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View article: Fused Specht polynomials and 𝑐=1 degenerate conformal blocks
Fused Specht polynomials and 𝑐=1 degenerate conformal blocks Open
We introduce a class of polynomials that we call fused Specht polynomials and use them to characterize irreducible representations of the fused Hecke algebra with parameter in the space of polynomials. We apply the fused Specht polynomial…
View article: Semiclassical limit of a non-polynomial q-Askey scheme
Semiclassical limit of a non-polynomial q-Askey scheme Open
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View article: Fused Specht Polynomials and $c=1$ Degenerate Conformal Blocks
Fused Specht Polynomials and $c=1$ Degenerate Conformal Blocks Open
We introduce a class of polynomials that we call fused Specht polynomials and use them to characterize irreducible representations of the fused Hecke algebra with parameter $q=-1$ in the space of polynomials. We apply the fused Specht poly…
View article: Planar UST Branches and $c=-2$ Degenerate Boundary Correlations
Planar UST Branches and $c=-2$ Degenerate Boundary Correlations Open
We provide a conformal field theory (CFT) description of the probabilistic model of boundary effects in the wired uniform spanning tree (UST) and its algebraic content, concerning the entire first row of the Kac table with central charge $…
View article: Semiclassical limit of a non-polynomial $q$-Askey scheme
Semiclassical limit of a non-polynomial $q$-Askey scheme Open
We prove a semiclassical asymptotic formula for the two elements $\mathcal M$ and $\mathcal Q$ lying at the bottom of the recently constructed non-polynomial hyperbolic $q$-Askey scheme. We also prove that the corresponding exponent is a g…
View article: On the Virasoro fusion and modular kernels at any irrational central charge
On the Virasoro fusion and modular kernels at any irrational central charge Open
We propose a series representation for the Virasoro fusion and modular kernels at any irrational central charge. Two distinct, yet closely related formulas are needed for the cases $c\in \mathbb C \backslash (-\infty,1]$ and $c <1$. Our pr…
View article: Non-polynomial q-Askey Scheme: Integral Representations, Eigenfunction Properties, and Polynomial Limits
Non-polynomial q-Askey Scheme: Integral Representations, Eigenfunction Properties, and Polynomial Limits Open
We construct a non-polynomial generalization of the q -Askey scheme. Whereas the elements of the q -Askey scheme are given by q -hypergeometric series, the elements of the non-polynomial scheme are given by contour integrals, whose integra…
View article: Degenerate conformal blocks for the $W_3$ algebra at c=2 and connection probabilities in the triple dimer model
Degenerate conformal blocks for the $W_3$ algebra at c=2 and connection probabilities in the triple dimer model Open
We study a homogeneous system of $d+8$ linear partial differential equations (PDEs) in $d$ variables arising from two-dimensional Conformal Field Theories (CFTs) with a $W_3$-symmetry algebra. In the CFT context, $d$ PDEs are third-order a…
View article: Non-polynomial $q$-Askey scheme: integral representations, eigenfunction properties, and polynomial limits
Non-polynomial $q$-Askey scheme: integral representations, eigenfunction properties, and polynomial limits Open
We construct a non-polynomial generalization of the $q$-Askey scheme. Whereas the elements of the $q$-Askey scheme are given by $q$-hypergeometric series, the elements of the non-polynomial scheme are given by contour integrals, whose inte…
View article: The family of confluent Virasoro fusion kernels and a non-polynomial $q$-Askey scheme
The family of confluent Virasoro fusion kernels and a non-polynomial $q$-Askey scheme Open
We study the recently introduced family of confluent Virasoro fusion kernels $\mathcal{C}_k(b,\boldsymbolθ,σ_s,ν)$. We study their eigenfunction properties and show that they can be viewed as non-polynomial generalizations of both the cont…
View article: Irregular conformal blocks and connection formulae for Painlevé V functions
Irregular conformal blocks and connection formulae for Painlevé V functions Open
We prove a Fredholm determinant and short-distance series representation of the Painlevé V tau function τt associated with generic monodromy data. Using a relation of τt to two different types of irregular c = 1 Virasoro conformal blocks a…
View article: On the connection problem for Painlevé I
On the connection problem for Painlevé I Open
We study the dependence of the tau function of Painlev\\'e I equation on the\ngeneralized monodromy of the associated linear problem. In particular, we\ncompute connection constants relating the tau function asymptotics on five\ncanonical …