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Dynamical interface above a hard wall and reflected SPDE on the half-line
Pierre Faug\`ere, Cyril Labb\'e
https://arxiv.org/abs/2509.03328 https://arxi…

Dynamical interface above a hard wall and reflected SPDE on the half-line
We consider a dynamical random interface on the infinite lattice $\mathbb{N}$ evolving according to a "corner flip" dynamic above a hard wall, with an additional pinning at the origin. We study the stationary fluctuations under a diffusive scaling and prove convergence in law towards the solution of an SPDE of Nualart-Pardoux's type, namely the Reflected Stochastic Heat Equation on the half-line. We also obtain that the law of the 3-dimensional Bessel process is an invariant measure for this SP…

Unitary representations attached to parabolic subgroups: the case of abelian unipotent radical
Dan Ciubotaru
https://arxiv.org/abs/2510.11862 https://arxiv…

Unitary representations attached to parabolic subgroups: the case of abelian unipotent radical
We classify the unitary representations with integral infinitesimal character in Lusztig's category of unipotent representations in the case when the geometric parameter space comes from the action of a Levi subgroup on the abelian nilradical of a (maximal) parabolic subalgebra. We organise the unitary representations into microlocal Arthur packets. This is a test case for investigating a conjectural description of unitary representations with integral infinitesimal character.