On the structure of free baxter algebras

AbstractA Baxter algebra is a commutative algebra A together with a linear operator P such that P(ab) + P(a) P(b) = P(aP(b)) + P(bP(a)) holds for any pair a, b in A. We construct in an explicit way the free Baxter algebra B(X) on a set X. A suitable completion B̂(X) of B(X) is the algebra of formal power series in the indeterminates Dn(χ) for n ⩾ 0 and χ in X, where D(a) = −∑∞j=1Pj(a), the series converging in B̂(X). Incidentally a new set of identities of combinatorial interest is derived

A CLT for Plancherel representations of the infinite-dimensional unitary group

We study asymptotics of traces of (noncommutative) monomials formed by images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge to (commutative) moments of a Gaussian process that can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields. The limiting process has previously arisen via the global scaling limit of spectra for submatrices of Wigner Hermitian random matrices. This note is an announcement, proofs will appear elsewhere.Comment: 12 page

Fourier Transforms of Lorentz Invariant Functions

Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail, and the results for 1+n dimensions are given.Comment: 15 pages, 1 figur

Operations on integral lifts of K(n)

This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence that operations on lifts of the functors K(n) to cohomology theories with values in modules over valuation rings of local number fields, indexed by Lubin-Tate groups of such fields, are extensions of the groups of automorphisms of the indexing group laws, by the exterior algebras on the normal bundle to the orbits of the group laws in the space of lifts.Comment: \S 2.0 hopefully less cryptic. To appear in the proceedings of the 2015 Nagoya conference honoring T Ohkawa. Comments very welcome

Uniform generation in trace monoids

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl