A one-parameter deformation of the Farahat-Higman algebra
نویسنده
چکیده
We show, by introducing an appropriate basis, that a one-parameter family of Hopf algebras introduced by Foissy [Adv. Math. 218 (2008) 136-162] interpolates beetween the Faà di Bruno algebra and the Farahat-Higman algebra. Its structure constants in this basis are deformation of the top connection coefficients, for which we obtain analogues of Macdonald’s formulas.
منابع مشابه
The Farahat-higman Ring of Wreath Products and Hilbert Schemes
We study the structure constants of the class algebra RZ(Γn) of the wreath products Γn associated to an arbitrary finite group Γ with respect to a basis provided by the conjugacy classes. A suitable filtration on the RZ(Γn) gives rise to the rings GΓ(n) with non-negative integer structure constants independent of n, which are then encoded in a single (Farahat-Higman) ring GΓ. We establish vario...
متن کاملDistance-regular graphs of q-Racah type and the q-tetrahedron algebra
In this paper we discuss a relationship between the following two algebras: (i) the subconstituent algebra T of a distance-regular graph that has q-Racah type; (ii) the q-tetrahedron algebra ⊠q which is a q-deformation of the three-point sl2 loop algebra. Assuming that every irreducible T -module is thin, we display an algebra homomorphism from ⊠q into T and show that T is generated by the imag...
متن کاملVertex Algebras and the Class Algebras of Wreath Products
The Jucys-Murphy elements for wreath products Γn associated to any finite group Γ are introduced and they play an important role in our study on the connections between class algebras of Γn for all n and vertex algebras. We construct an action of (a variant of) the W1+∞ algebra acting irreducibly on the direct sum RΓ of the class algebras of Γn for all n in a group theoretic manner. We establis...
متن کاملA One-parameter Deformation of the Noncommutative Lagrange Inversion Formula
We give a one-parameter deformation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder-Frabetti-Krattenthaler for the antipode of the noncommutative Faá di Bruno algebra. Namely, we obtain a closed formula for the antipode of the one-parameter deformation of this Hopf algebra discovered by Foissy.
متن کامل1 9 Se p 20 06 A multipurpose Hopf deformation of the Algebra of Feynman - like Diagrams
We construct a three parameter deformation of the Hopf algebra LDIAG. This new algebra is a true Hopf deformation which reduces to LDIAG on one hand and to MQSym on the other , relating LDIAG to other Hopf algebras of interest in contemporary physics. Further , its product law reproduces that of the algebra of polyzeta functions .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 32 شماره
صفحات -
تاریخ انتشار 2011