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THE BASE CHANGE FUNDAMENTAL LEMMA FOR CENTRAL ELEMENTS IN PARAHORIC HECKE ALGEBRAS
PARAHORIC HECKE Algebra
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2015/9/29
Let G be an unramified group over a p-adic field F, and let E/F be a finite
unramified extension field. Let θ denote a generator of Gal(E/F). This paper concerns the
ma...
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
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2015/8/17
This talk is about aspects of representation theory of padic
groups that parallel real groups. In the case of real groups, the
results refer to J. Adams, P. Trapa, M. vanLeuwen, W-L. Yee a...
Hermitian and Unitary Representations for Affine Hecke Algebras
Affine Hecke Algebras Hermitian and Unitary
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2015/8/17
This talk is about aspects of representation theory of padic
groups that parallel real groups. This conforms to the Lefschetz
principle which states that what is true for real groups is al...
GALOIS CONNECTIONS FOR INCIDENCE HOPF ALGEBRAS OF PARTIALLY ORDERED SETS.
Incidence Hopf algebras Galois connections
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2015/8/14
An important well-known result of Rota describes the relationship between the M¨obius
functions of two posets related by a Galois connection. We present an analogous result relating
the antipodes of...
A NOTE ON STRONGLY SEPARABLE ALGEBRAS
Separable algebras invariants coinvariants coalgebras Hopf algebras
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2015/8/14
Let A be an algebra over a field k. If M is an A–bimodule, we let
MA and MA denote respectively the k–spaces of invariants and coinvariants of
M, and 'M : MA
! MA be the natural map. In this note w...
PREPOISSON ALGEBRAS
prelie algebras zinbiel algebras dendriform algebras Baxter operators
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2015/8/14
A definition of prepoisson algebras is proposed, combining structures of prelie and zinbiel
algebra on the same vector space. It is shown that a prepoisson algebra gives rise to a Poisson algebra
by...
Infinitesimal Hopf algebras
Hopf algebras derivations Yang-Baxter equation Drinfeld’s double
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2015/8/14
Infinitesimal bialgebras were introduced by Joni and Rota [J-R].
An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in
such a way that the comultiplication is a derivation. I...
INFINITESIMAL BIALGEBRAS, PRE-LIE AND DENDRIFORM ALGEBRAS
Infinitesimal bialgebras pre-Lie algebras dendriform algebras
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2015/8/14
We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal
bialgebra. We show that they correspond to modules and bimodules over the infinitesimal
version of the d...
QUADRI-ALGEBRAS
quadri-algebra operad Koszul duality
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2015/8/14
We introduce the notion of quadri-algebras. These are associative algebras
for which the multiplication can be decomposed as the sum of four operations
in a certain coherent manner. We present sever...
Representations of matched pairs of groupoids and applications to weak Hopf algebras
groupoids and applications algebras
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2015/8/14
We introduce the category of set-theoretic representations of a
matched pair of groupoids. This is a monoidal category endowed with a
monoidal functor f` to the category of quivers over the common b...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
Hopf algebr rooted tree planar binary tree symmetric group
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2015/8/14
Consider the coradical filtrations of the Hopf algebras of planar binary
trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We
give explicit isomorphisms showing that the asso...
COMBINATORIAL HOPF ALGEBRAS AND GENERALIZED DEHN-SOMMERVILLE RELATIONS
Hopf algebra, character, generalized Dehn-Sommerville relations
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2015/8/14
A combinatorial Hopf algebra is a graded connected Hopf algebra over
a field k equipped with a character (multiplicative linear functional) : H → k.
We show that the terminal object in the categor...
Coxeter groups and Hopf algebras I
Coxeter group descent global descent hyperplane arrangement
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2015/8/14
In the study of a mathematical system, algebraic structures allow for the discovery of
more information. This is the motor behind the success of many areas of mathematics
such as algebraic geometry,...
THE PEAK ALGEBRA AND THE DESCENT ALGEBRAS OF TYPES B AND D
peak algebra signed permutations Coxeter groups
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2015/8/14
We show the existence of a unital subalgebra Pn of the symmetric group
algebra linearly spanned by sums of permutations with a common peak set, which we
call the peak algebra. We show that Pn is the...
Monoidal Functors, Species and Hopf Algebras
bilax monoidal functor Fock functor Hopf algebra
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2015/8/14
The fact that α is a morphism of lax monoidal functors is the same as (6.4) and the
coassociativity of I in (6.8). The fact that λ and ρ are morphisms of lax functors
is the same as (6.6) and the c...