» Pop-Stack Operators for Torsion Classes and Cambrian Lattices. (arXiv:2312.03959v1 [math.CO])

08/12/23 10:01 from math.RT updates on arXiv.org

The pop-stack operator of a finite lattice $L$ is the map $\mathrm{pop}^{\downarrow}_L\colon L\to L$ that sends each element $x\in L$ to the meet of $\{x\}\cup\text{cov}_L(x)$, where $\text{cov}_L(x)$ is the set of elements covered by $x...

» N-spherical functors and tensor categories. (arXiv:2312.03972v1 [math.CT])

08/12/23 10:01 from math.RT updates on arXiv.org

We apply the recently introduced notion, due to Dyckerhoff, Kapranov and Schechtman, of $N$-spherical functors of stable infinity categories, which generalise spherical functors, to the setting of monoidal categories. We call an object $...

» Depth Zero Supercuspidal Representations of Classical Groups into L-packets: the Typically Almost Symmetric Case. (arXiv:2312.04061v1 [math.RT])

08/12/23 10:01 from math.RT updates on arXiv.org

We classify what we call ``typically almost symmetric'' depth zero supercuspidal representations of classical groups into L-packets. Our main results resolve an ambiguity in the paper of Lust-Stevens \cite{Lust-Stevens} in this case, whe...

» Para-spaces, their differential analysis and an application to Green's quantisation. (arXiv:2312.04250v1 [math-ph])

08/12/23 10:01 from math.RT updates on arXiv.org

We introduce a class of non-commutative geometries, loosely referred to as para-spaces, which are manifolds equipped with sheaves of non-commutative algebras called para-algebras. A differential analysis on para-spaces is investigated, w...

» Torsion-simple objects in abelian categories. (arXiv:2312.04384v1 [math.RT])

08/12/23 10:01 from math.RT updates on arXiv.org

We introduce the notion of torsion-simple objects in an abelian category: these are the objects which are always either torsion or torsion-free with respect to any torsion pair. We present some general results concerning their properties...

» The valuation pairing on an upper cluster algebra. (arXiv:2204.09576v2 [math.RT] UPDATED)

08/12/23 10:01 from math.RT updates on arXiv.org

It is known that many (upper) cluster algebras are not unique factorization domains. We exhibit the local factorization properties with respect to any given seed $t$: any non-zero element in a full rank upper cluster algebra can be uniqu...

» Spectral properties of the Bloch-Torrey operator in three dimensions. (arXiv:2312.04200v1 [math-ph])

08/12/23 10:01 from math.SP updates on arXiv.org

We consider the Bloch-Torrey operator, $-\Delta + igx$, that governs the time evolution of the transverse magnetization in diffusion magnetic resonance imaging (dMRI). Using the matrix formalism, we compute numerically the eigenvalues an...

» A spectral condition for the control of eigenfunctions of Baouendi-Grushin type operators. (arXiv:2312.04359v1 [math.SP])

08/12/23 10:01 from math.SP updates on arXiv.org

We study a concentration inequality for eigenfunctions of a Baouendi-Grushin operator on a cylinder or a torus. Using separation of variables, we prove that this inequality holds under a spectral multiplicity condition. Using Albert-Uhle...