Related papers: Dyadic bi-parameter simple commutator and dyadic l…
We prove that a quasi-isomorphism $f : A \to B$ between commutative DG rings, where $B$ admits a divided power structure, can be factored as $f = \tilde{f} \circ e$, where $e : A \to \tilde{B}$ is a split injective quasi-isomorphism, and…
We show in a precise way, either in the fermionic or its bosonized version, that Bose symmetry provides a systematic way to carry out the chiral decomposition of the two dimensional fermionic determinant. Interpreted properly, we show that…
Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in…
The question if a Mott insulator and a band insulator are fundamentally different has been the matter of intensive research recently. Here we consider a simple model which allows by tuning one parameter to go continously from a Mott…
In this paper we investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $\mu,\lambda\in A_{p,q}$ and $\alpha/n+1/q=1/p$, the norm $\|…
We present a new, elementary proof of Boyd's interpolation theorem. Our approach naturally yields a noncommutative version of this result and even allows for the interpolation of certain operators on l^1-valued noncommutative symmetric…
We revisit the rare leptonic decay $B_s \to \mu^+ \mu^-$ in the two-Higgs doublet models with a softly broken $Z_2$ symmetry, namely type-I, type-II, type-X and type-Y 2HDMs. We have derived the relevant full one-loop Wilson coefficients of…
Let $(X, d)$ be a semimetric space. A permutation $\Phi$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f \colon d(X^2) \to d(X^2)$ such that $$ d(x, y) = f(d(\Phi(x), \Phi(y))) $$ for all…
We prove that every simple transitive $2$-representation of the fiat $2$-category of Soergel bimodules (over the coinvariant algebra) in type $B_2$ is equivalent to a cell $2$-representation. We also describe some general properties of the…
If a reduced bivariate polynomial is quasi-homogeneous, then its discriminant is a monomial. Over fields of characteristic $0$, we show that if one adds another simple condition, this becomes an equivalence. We also give a third equivalent…
Using Wilson's Haar basis in $\R^n$, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in $\R^n$. We can then extend "trivially" Beznosova's Bellman function proof of the linear…
We explore commutativity up to a factor, $AB=\lambda BA$, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor $\lambda$ are formulated and shown to depend on spectral properties of the operators…
The Bogoliubov transformation is generally derived in the context of identical bosons with the use of ``second quantized'' a and $a^{\dagger}$ operators (or, equivalently, in field theory). Here, we show that the transformation, together…
The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The…
We give new and elementary proofs of one weight norm inequalities for fractional integral operators and commutators. Our proofs are based on the machinery of dyadic grids and sparse operators used in the proof of the A2 conjecture.
We describe a general framework for notions of commutativity based on enriched category theory. We extend Eilenberg and Kelly's tensor product for categories enriched over a symmetric monoidal base to a tensor product for categories…
The $B_N$-type Calogero-Sutherland-Moser system in one-dimension is shown to be equivalent to a set of decoupled oscillators by a similarity transformation. This result is used to show the connection of the $A_N$ and $B_N$ type models and…
In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators $T_b^m$. Our results are new even for the first order commutator $T_b^1$. A new bump type…
In this paper we introduce a property of ergodic flows, called Property B. We prove that any ergodic hyperfinite equiva- lence relation of type III_o whose associated flow satisfies this property is not of product type. A consequence of…
We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with a separable dual.