Related papers: Quotient singularities by permutation actions are …

We shall investigate index 1 covers of 2-dimensional log terminal singularities. The main result is that the index 1 cover is canonical if the characteristic of the base field is different from 2 or 3. We also give some counterexamples in…

The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…

In this paper, we study Lie-Rinehart cohomology for quotients of singularities by finite groups, and interpret these cohomology groups in terms of integrable connection on modules.

Let $G$ be a finite group and $K$ a finite field of characteristic $2$. Denote by $t$ the $2$-rank of the commutator factor group $G/G'$ and by $s$ the number of self-dual simple $KG$-modules. Then the Witt group of equivariant quadratic…

We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.

We derive a uniqueness result for non-Cartesian composition of systems in a large class of process theories, with important implications for quantum theory and linguistics. Specifically, we consider theories of wavefunctions valued in…

We give explicit computations of the $\Gamma$-Euler characteristic of several families of orbit space definable translation groupoids. These include the translation groupoids associated to finite-dimensional linear representations of the…

There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…

We present a new relation between an invariant of singularities in characteristic zero (the log canonical threshold) and an invariant of singularities defined via the Frobenius morphism in positive characteristic (the F-pure threshold). We…

We show that the quantum coordinate ring of a semisimple group is a unique factorisation domain in the sense of Chatters and Jordan in the case where the deformation parameter q is a transcendental element.

In this paper, we connect two types of representations of a permutation $\sigma$ of the finite field $\F_q$. One type is algebraic, in which the permutation is represented as the composition of degree-one polynomials and $k$ copies of…

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…

In commuting parametric quantum circuits, the Fourier series of the pairwise fidelity can be expressed as the characteristic function of random variables. Furthermore, expressiveness can be cast as the recurrence probability of a random…

A quantum characteristic exponent may be defined, with the same operational meaning as the classical Lyapunov exponent when the latter is expressed as a functional of densities. Existence conditions and supporting measure properties are…

A singularity in characteristic zero is said to be of dense F-pure type if its modulo p reduction is locally F-split for infinitely many p. We prove that if $x \in X$ is an isolated log canonical singularity with $\mu(x \in X) \le 2$ (see…

The study of $G$-equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear $G$-equivariant operator can be produced by a suitable permutant measure,…

We introduce and study a log discrepancy function on the space of semivaluations centered on an integral noetherian scheme of positive characteristic. Our definition shares many properties with the analogue in characteristic zero; we prove…

We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains…

We study logarithmic jet schemes of a log scheme and generalize a theorem of M. Mustata from the case of ordinary jet schemes to the logarithmic case. If X is a normal local complete intersection log variety, then X has canonical…

We show that the only sporadic simple group such that some of its faithful representations or some faithful representations of its stem extensions give rise to exceptional (weakly-exceptional but not exceptional, respectively) quotient…