Combinatorics of $\phi$-deformed stuffle Hopf algebras

Combinatorics of $φ$-deformed stuffle Hopf algebras

3 General results on summability and duality 4 3.1 Total algebras and duality . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 Series and infinite sums . . . . . . . . . . . . . . . . . . . 4 3.1.2 Summable families in Hom spaces. . . . . . . . . . . . . . 5 3.1.3 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Theorem of Cartier-Quillen-Milnor-Moore (analytic form) . ....

Combinatorics of / / / φ -

In order to extend the Schützenberger’s factorization to general perturbations, the combinatorial aspects of the Hopf algebra of the φ-deformed stuffle product is developed systematically in a parallel way with those of the shuffle product. and in emphasizing the Lie elements as studied by Ree. In particular, we will give an effective construction of pair of bases in duality.

Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras

Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed bose and fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Gree...

On the Coderivations of Some Hopf Algebras

A ug 2 00 9 SKEW LITTLEWOOD - RICHARDSON RULES FROM HOPF ALGEBRAS

Assaf and McNamara [1] recently used combinatorics to give an elegant and surprising formula for the product of a skew Schur function by a complete homogeneous symmetric function. Their paper included an appendix by one of us (Lam) with a simple algebraic proof of their formula, and also a conjectural skew version of the Littlewood-Richardson rule. We show how these formulas and much more are s...