Before Einstein’s publication in 1905 of his theory of special relativity, the mathematical manipulations that were a product of his theory were in fact already known. The so called Lorentz transformations were tricks that had been found that allowed the speed of light to propagate in all directions at the same speed, which accounted for its strange behavior when traveling through the now infam...

The concepts of minimal clinically important improvement (MCII) and patient acceptable symptomatic state (PASS) could help in interpreting results of trials involving patient-reported outcomes by translating the response at the group level (change in mean scores) into more clinically meaningful information by addressing the patient level as "therapeutic success (yes/no)." The aims of the specia...

We give a formula for the character of the representation of the Weyl group Sn on each isotypic component of the cohomology of the set of regular elements of a maximal torus of SLn, with respect to the action of the centre. As a consequence, we find that this representation is induced from a cohomology representation of a wreath product subgroup.

Given a word W in the free group on 2 letters F2, Horowitz showed that the special linear character of W is an integer polynomial in the 3 characters of the basic words of F2. Special linear characters are defined via the trace of their representations, and the polynomial character of an arbitrary W can be found by application of certain “trace relations”, which allow one to write the character...

Abstract. A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a “canonical basis” for every finite dimensional irreducible Uq(sl(n))-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quan...

We prove that for any infinite field F , the map H3(SLn(F ), Z)→ H3(SLn+1(F ), Z) is an isomorphism for all n ≥ 3. When n = 2 the cokernel of this map is naturally isomorphic to 2 · K 3 (F ), where K n (F ) is the nth Milnor K-group of F . We deduce that the natural homomorphism from H3(SL2(F ), Z) to the indecomposable K3 of F , K3(F ), is surjective for any infinite field F .

In this note, we establish a connection between the dynamical degree, or algebraic entropy of a certain class of polynomial automorphisms of R3, and the maximum topological entropy of the action when restricted to compact invariant subvarieties. Indeed, when there is no cancellation of leading terms in the successive iterates of the polynomial automorphism, the two quantities are equal. In gene...

Let F be a field of characteristic zero and let ft,n be the stabilization homomorphism Hn(SLt(F ), Z) → Hn(SLt+1(F ), Z). We prove the following results: For all n, ft,n is an isomorphism if t ≥ n + 1 and is surjective for t = n, confirming a conjecture of C-H. Sah. Furthermore if n is odd, then fn,n is an isomorphism. If n ≥ 1 is even then the cokernel of fn−1,n is naturally isomorphic to the ...