1,762 research outputs found
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
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