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CANONICAL CHARACTERS ON QUASI-SYMMETRIC FUNCTIONS AND BIVARIATE CATALAN NUMBERS
Hopf algebra character quasi-symmetric function central binomial coefficient
2015/8/14
Every character on a graded connected Hopf algebra decomposes uniquely as
a product of an even character and an odd character [2]. We obtain explicit formulas for
the even and odd parts of the unive...
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
noncommuting variables related Hopf algebras
2015/8/14
We identify two seemingly disparate structures: supercharacters, a useful way of doing
Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite
field, and th...
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
The coefficient matrix and symmetric function hopf algebra
2015/7/7
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a fi-nite ...
The Hopf algebra of odd symmetric functions
odd symmetric functions Hopf algebra Quantum Algebra
2011/9/22
Abstract: We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd sy...
Loop symmetric functions and factorizing matrix polynomials
Loop symmetric functions factorizing matrix polynomials
2011/1/18
These are notes for my talk at ICCM 2010, Beijing. We survey some results, obtained jointly with Pavlo Pylyavskyy, concerning the ring of loop symmetric functions. Motivations from networks on surface...
Generalizing Tanisaki's ideal via ideals of truncated symmetric functions
Generalizing Tanisaki's ideal ideals of truncated symmetric functions
2011/1/19
We de ne a family of ideals Ih in the polynomial ring Z[x1; x2; : : : ; xn] that are
parametrized by Hessenberg functions h (equivalently Dyck paths or ample partitions). The
ideals Ih generalize al...
Polytopes, Hopf algebras and Quasi-symmetric functions
Polytopes Hopf algebras Quasi-symmetric functions
2010/11/11
In this paper we use the technique of Hopf algebras and quasi-symmetric functions to study the combinatorial polytopes. Consider the free abelian group $\mathcal{P}$ generated by all combinatorial po...
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
Supercharacters symmetric functions noncommuting variables related Hopf algebras
2010/12/9
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite
field, and the...
Laguerre and Meixner symmetric functions, and infinite-dimensional diffusion processes
Laguerre Meixner symmetric functions infinite-dimensional diffusion processes
2010/12/3
The Laguerre symmetric functions introduced in the note are indexed by arbitrary partitions and depend on two continuous parameters. The top degree homogeneous component of every Laguerre symmetric fu...
Stable Equivalence Over Symmetric Functions
Giambelli-type matrix Jacobi-Trudi matrix dual Jacobi-Trudi matrix stably equivalent outside decomposition cutting strip twist transformation
2014/6/3
By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli-type matrices for a given skew Schur function are stably equivalent to each other ov...