Related papers: Inductive AM condition for the alternating groups …

We give new criteria for the irreducibility of parabolic induction on the general linear group and its inner forms over a local non-archimedean field. In particular, we give a necessary and sufficient condition when the inducing data is of…

For a field $K$ of characteristic different from 2, we find the explicit form of the minimal idempotents of the twisted group algebra $K_t< g>$ of a cyclic 2-group $<g>$ over $K$.

We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…

For k a field of characteristic 2, we show that there is a unique continuous automorphism of order 4 of the power series ring k[[t]] which sends t to t + t^2 + (t^6) + (t^{12} + t^{14}) + (t^{24} + t^{26} + t^{28} + t^{30}) + ... . For j >=…

It is established that if a time series satisfies the Berman condition, and another related (summability) condition, the result of filtering that series through a certain type of filter also satisfies the two conditions. In particular it…

Using the calculus of Steenrod operations in \'etale cohomology developed in [Feng17], we prove that the analogue of Tate's pairing on higher Brauer groups is alternating on 2-torsion. This improves upon a result of Jahn [Jahn15, Math.…

We determine the quadratic type of the 2-modular principal indecomposable modules of the double covers of alternating groups.

We prove that the inertia groups of all sufficiently-connected, high-dimensional $(2n)$-manifolds are trivial. This is a key step toward a general classification of manifolds in the metastable range. Specifically, for $m \gg 0$ and…

We give an application of Mumford's theory of canonical theta characteristics to a Diophantine problem in characteristic two. We prove that a smooth plane curve over a global field of characteristic two is defined by the determinant of a…

In this note, we give a group-theoretic condition which is equivalent to the fact that the trivial character is the only complex irreducible character of a finite group G which is contained in the principal p-block for each prime p in a…

We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of…

Let B be a p-block of a finite group G with abelian defect group D such that S\unlhd G, S'=S, G/Z(S)\le\Aut(S) and S/Z(S) is a sporadic simple group. We show that B is isotypic to its Brauer correspondent in N_G(D) in the sense of Brou\'e.…

This paper is devoted to the analysis of an abstract formula describing quantum adiabatic charge pumping in a general context. We consider closed systems characterized by a slowly varying time-dependent Hamiltonian depending on an external…

The simplicity of the induced modules for reductive Lie algebras over an algebraically closed field of positive characteristic is studied, and a necessary and sufficient condition for the simplicity is given.

We write down two E11 invariant conditions which at low levels reproduce the known half BPS conditions for type II theories. These new conditions contain, in addition to the familiar central charges, an infinite number of further charges…

We study collections of additive categories $\mathcal{M}(G)$, indexed by finite groups $G$ and related by induction and restriction in a way that categorifies usual Mackey functors. We call them `Mackey 2-functors'. We provide a large…

By stating the adiabatic theorem of quantum mechanics in a clear and rigorous way, we establish a necessary condition and a sufficient condition for its validity, where the latter is obtained employing our recently developed adiabatic…

The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lison\v{e}k states that by inserting all cyclic permutations of some initial blocks of 2's into the multiple zeta value $ \zeta(1,3,\ldots,1,3) $ and summing, one obtains…

We prove that for most groups of Lie type, the bijections used by Malle and Spaeth in the proof of Isaacs-Malle-Navarro's inductive McKay conditions for the prime 2 and odd primes dividing q - 1 are also equivariant with respect to certain…

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…