Fields Working Sessions Tuesdays 12:00 p.m. - 1:30 p.m., unless otherwise
indicated.
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3-Apr-2007
12:00 p.m.
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Franco Saliola, UQAM
Finding the Quiver of the Descent Algebras
This will be a survey outlining the current status of my project to study
of the representation theory of the descent algebra of a finite Coxeter
group. It will concentrate on the descent algebra of the symmetric group
because the current results are better in this case. The approach utilizes
what I call the "geometric approach" to the descent algebra:
there is a semigroup algebra constructed from the reflection arrangement
of the Coxeter group that contains the descent algebra. The quiver of
this semigroup algebra will be constructed and it will be used to get
information about the quiver of the descent algebra. |
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27-Mar-2007
12:00 p.m.
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Nantel Bergeron, York University
Working Session: Finding knuth relations for a type B Robinson Schensted
corespondence invoving Domino tableaux |
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27-Feb-2007
12:00 p.m.
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Nantel Bergeron, York University
Generalization of the weak order on tableaux to Coxeter groups and
related problems II |
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20-Feb-2007
12:00 p.m.
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Nantel Bergeron, York University
Working Session: Generalization of the weak order on tableaux to Coxeter
groups and related problems |
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13-Feb-2007
12:00 p.m.
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Special Session
Srecko Brlek, UQAM
Variations on Cantor's celebrated diagonal argument
Given a square $n \times n$ tableau $T=\left(a_i^j\right)$ on a finite
alphabet $A$, let $L $ be the set of its row-words. The permanent $\Perm(T)$
is the set of words $a_{\pi(1)}^1a_{\pi(2)}^2\cdots a_{\pi(n)}^n$, where
$\pi$ runs through the set of permutations of $n$ elements. Cantorian
tableaux are those for which $\Perm(T)\cap L=\emptyset.$ Let $s=s(n)$
be the cardinality of $A$. We show in particular that for large $n$, if
$s(n) <(1-\epsilon) n/\log n$ then most of the tableaux are non-Cantorian,
whereas if $s(n) >(1+\epsilon) n/\log n$ then most of the tableaux
are Cantorian. We conclude our article by the study of infinite tableaux.
Consider for example the infinite tableaux whose rows are the binary expansions
of the real algebraic numbers in the unit interval. We show that the permanent
of this tableau contains exactly the set of binary expansions of all the
transcendental numbers in the unit interval. |
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12-Feb-2007
12:00 p.m.
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Special Session
Amy Glen, CRM-ISM-LaCIM, UQAM
Characterizations of finite and infinite episturmian words via lexicographic
orderings
In this talk, I will present some new results arising from collaborative
work with Jacques Justin (France) and Giuseppe Pirillo (Italy). This work,
which extends previous results on extremal properties of infinite Sturmian
and episturmian words, is purely combinatorial in nature. Specifically,
we characterize by lexicographic order all finite Sturmian and episturmian
words, i.e., all (finite) factors of such infinite words. Consequently,
we obtain a characterization of infinite episturmian words in a wide sense
(episturmian and episkew infinite words). That is, we characterize the
set of all infinite words whose factors are (finite) episturmian. Similarly,
we characterize by lexicographic order all balanced infinite words over
a 2-letter alphabet; in other words, all Sturmian and skew infinite words,
the factors of which are (finite) Sturmian.
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06-Feb-2007
12:00 p.m.
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Muge Taskin, York University and Fields
Problems on the weak order on tableaux, proofs II |
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30-Jan-2007
12:00 p.m.
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Muge Taskin, York University and Fields
Problems on the weak order on tableaux, proofs I |
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23-Jan-2007
12:00 p.m.
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Hugh Thomas, U. New Brunswick
Schiffler's formula for A_n cluster variables and some generalizations
We will present Schiffler's formula for expanding a cluster variable as
a sum of Laurent monomials in the seed variables in the A_n case (as presented
in math.RT/0611956). We will discuss a generalization in the context of
Fomin-Shapiro-Thurston cluster algebras associated to surfaces, and a
related result in which, for an acyclic seed, we give a formula to expand
a cluster variables as a sum of standard monomials in the lower cluster
algebra. The new results we will be discussing are joint with Ralf Schiffler.
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16-Jan-2007
12:00 p.m.
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Mike Zabrocki
Decomposition of a Gl_n irrep into S_n irreps, Part 3
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12-Dec-2006
12:00 p.m.
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Alejandra Premat
Part II of Crystal Bases
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05-Dec-2006
12:00 p.m.
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Mike Zabrocki
Decomposition of a Gl_n irrep into S_n irreps (data
for n=6) (some conjectures and results) |
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28-Nov-2006
12:00 p.m.
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Muge Taskin, York University and Fields
Solution to open problems |
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21-Nov-2006
12:00 p.m.
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Muge Taskin, York University and Fields
Open problems related to some orders on standard Young tableaux part 3
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14-Nov-2006
12:00 p.m.
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Mike Zabrocki
An explanation of a problem of
computing the restriction of a Gl_n module
to S_n.
Remark: it is true that F_{S_n}( f g ) = F_{S_n}(f) * F_{S_n}(g) (example)
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07-Nov-2006
12:00 p.m.
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Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, isometry problem: proof
Part 2
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31-Oct-2006
12:00 p.m.
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Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, isometry problem: proof
Part 1
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24-Oct-2006
12:00 p.m.
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Muge Taskin, York University and Fields
Open problems related to some orders on standard Young tableaux Part
2
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17-Oct-2006
12:00 p.m.
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Muge Taskin, York University and Fields
Open problems related to some orders on standard Young tableaux Part
1 |
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10-Oct-2006
12:00 p.m.
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Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, open problems Part 2
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03-Oct-2006
11:00 a.m.
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Special Session
Christian Kassel, CNRS-Université Louis Pasteur, Strasbourg
A Hall algebra based on the projective line
(Joint work with Pierre Baumann)
One can construct a Hall algebra out of the vector bundles over a projective
curve on a finite field. I'll describe this algebra in the case when the
curve is a projective line. This algebra is related to the quantum affine
algebra associated to the Lie algebra sl(2). In my talk I'll insist on
the combinatorial aspects of the subject.
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26-Sep-2006
12:00 p.m.
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Alejandra Premat, York University and
Fields
Introduction to Crystal basis |
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19-Sep-2006
12:00 p.m.
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Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, open problems
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