Related papers: Schur-Weyl duality in positive characteristic
Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical…
A property of a filter, a kind of large cardinal property, suffices for the proof in Liu Shelah [LiSh:484] and is proved consistent as required there. A natural property which looks better, not only is not obtained here, but is shown to be…
An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.
We comment on one of the earliest derivations of the so-called wave-particle duality relation. Our aim is to point out a slight technical flaw in the proof, fixing it. Neither the physical content of the duality relation nor its validity is…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
Flat-space conformal invariance and curved-space Weyl invariance are simply related in dimensions greater than two. In two dimensions the Liouville theory presents an exceptional situation, which we here examine.
We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely and finitely many variables.
We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases: (1) Using a Schur-Weyl duality between a two-parameter quantum group and a…
This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economically and in a uniform way, categories ofstructures dually…
We determined the $\tau$-tilting finiteness of Schur algebras over an algebraically closed field of arbitrary characteristic, except for a few small cases.
In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this…
We prove vanishing of the higher direct images of the structure (and the canonical) sheaf for a proper birational morphism with source a smooth variety and target the quotient of a smooth variety by a finite group of order prime to the…
We give new proofs of two basic results in number theory: The law of quadratic reciprocity and the sign of the Gauss sum. We show that these results are encoded in the relation between the discrete Fourier transform and the action of the…
Let $k$ be a field of positive characteristic $p$, and $X$ be a separated of finite type $k$-scheme of dimension $d$. We construct a cycle map from the additive cycle complex to the residual complex of Serre-Grothendieck coherent duality…
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
Currently there are several approaches to resolution of singularities in positive characteristic all of which have hit some obstruction. One natural idea is to try to construct new meaningful examples at this point to gain a wider range of…
Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative…
This report consists of two parts. The first part is a brief exposition of classical descriptive set theory. This part introduces some fundamental concepts, motivations and results from the classical theory and ends with a section on the…
We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of Strengthened Cauchy-Schwarz inequalities is derived using these identities. Also, an…