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For a fixed double triangle lattice in a finite factor, we show that the subgroup of automorphisms of the factor leaving invariant the reflexive lattice generated by the double triangle lattice is isomorphic to a closed subgroup of SO(3). In particular, if the nontrivial projections in the...
It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated if there exists an intermediate sequence, containing a point from each hyperbolic geodesic which connects any two points from the original sequence, and whose separated...
We utilise recent results about the transcendental solutions to Riccati differential equations to provide a comprehensive description of the nature of the transcendental solutions to algebraic first‐order differential equations of genus zero.
For a finite‐dimensional algebra A, we establish correspondences between torsion classes and wide subcategories in mod(A). In case A is representation finite, we obtain an explicit bijection between these two classes of subcategories. Moreover, we translate our results to the language of ring...
Let F be a non‐archimedean local field, and n1 and n2 two positive even integers. We prove that if π1 and π2 are two smooth representations of GL(n1,F) and GL(n2,F) respectively, both admitting a Shalika functional, then the normalised parabolically induced representation π1×π2 also admits a...
We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by the first two Alexander polynomials. From this point of...
Let G be a finite group and let p be a prime. Assume that there exists a prime q dividing |G| which does not divide the order of any p‐local subgroup of G. If G is p‐solvable or q divides p−1, then G has a p‐block of defect zero. The case q=2 is a well‐known result by Brauer and Fowler.
The notion of central stability was first formulated for sequences of representations of the symmetric groups by Putman. A categorical reformulation was subsequently given by Church, Ellenberg, Farb, and Nagpal using the notion of FI‐modules, where FI is the category of finite sets and injective...
We study Schatten–von Neumann properties of multiple operator integrals with integrands in the Haagerup tensor product of L∞ spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten–von Neumann estimates in the case of Haagerup‐like tensor products.
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