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Autor:
Rioux, A. V., Nsimba-Batomene, T. R., Slimani, S., Bergeron, N. A. D., Gravel, M. A. M., Schreiber, S. V., Fiola, M. J., Haydock, L., Garneau, A. P., Isenring, P.
Publikováno v:
Physiological Reviews; Jul2024, Vol. 104 Issue 3, p1147-1204, 58p
Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for PGL(3,C)-representations. In particular we p
Externí odkaz:
http://arxiv.org/abs/1307.8343
Publikováno v:
International J. of Algebra {\bf 4-21} (2010) 1003--1020
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.
Externí odkaz:
http://arxiv.org/abs/0909.1112
Publikováno v:
Adv. in Appl. Math. 44 (2010), no. 1, 16--36
We define new generalizations of (q,t)-Catalan numbers applying nabla operator on k-Schur functions indexed by column partitions. In some special cases, we give a combinatorial interpretation of these numbers using configurations of Dyck paths. In so
Externí odkaz:
http://arxiv.org/abs/0806.3046
Publikováno v:
Discrete Math. 309 (2009), no. 16, 5092-5105
We introduce non-commutative analogues of $k$-Schur functions of Lapointe-Lascoux and Morse. We give an explicit formulas for the expansions of non-commutive functions with one and two parameters in terms of these new functions. These results are sim
Externí odkaz:
http://arxiv.org/abs/0804.0944
Autor:
Bergeron, N., van Willigenburg, S. J.
Publikováno v:
J. of Algebra 206:699-705 (1998)
Here we give a combinatorial interpretation of Solomon's rule for multiplication in the descent algebra of Weyl groups of type $D$, $\Sigma D_n$. From here we show that $\Sigma D_n$ is a homomorphic image of the descent algebra of the hyperoctahedral
Externí odkaz:
http://arxiv.org/abs/0706.2711
Autor:
Bergeron, N.
For abelian varieties $A$, in the most interesting cohomology theories $H^* (A)$ is the exterior algebra of $H^1(A)$. In this paper we study a weak generalization of this in the case of arithmetic manifolds associated to orthogonal or unitary groups.
Externí odkaz:
http://arxiv.org/abs/math/0612447
Autor:
Bergeron, N.
We give a new proof of a Theorem of Vogan which classify the cohomological representations of a real semisimple Lie group $G$ which are isolated in the unitary dual of $G$. We investigate the same question in the automorphic dual, and obtain partial
Externí odkaz:
http://arxiv.org/abs/math/0511689
Autor:
Bergeron, N.
Let $G$ be a connected semisimple group over ${\Bbb Q}$. Given a maximal compact subgroup and a convenient arithmetic subgroup $\Gamma\subset G({\Bbb Q})$, one constructs an arithmetic manifold $S=S(\Gamma)=\Gamma\backslash X$. If $H\subset G$ is a c
Externí odkaz:
http://arxiv.org/abs/math/0503062