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pro vyhledávání: '"Thomas Gobet"'
Autor:
Thomas Gobet
Publikováno v:
Journal of Algebra. 607:260-289
The submonoid of the 3-strand braid group B 3 generated by σ 1 and σ 1 σ 2 is known to yield an exotic Garside structure on B 3 . We introduce and study an infinite family ( M n ) n ≥ 1 of Garside monoids generalizing this exotic Garside structu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7d29790fefe0bffb0dc2a117d4d4fb8d
https://doi.org/10.1016/j.jalgebra.2021.04.014
https://doi.org/10.1016/j.jalgebra.2021.04.014
Autor:
Thomas Gobet
Publikováno v:
Algebras and Representation Theory. 24:169-201
We introduce bijections between generalized type An noncrossing partitions (that is, associated to arbitrary standard Coxeter elements) and fully commutative elements of the same type. The latter index the diagram basis of the classical Temperley–L
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::560f908785c84d6d3d704edc3b8d6b10
https://doi.org/10.1007/s10468-019-09940-1
https://doi.org/10.1007/s10468-019-09940-1
Publikováno v:
Representation Theory. An Electronic Journal of the American Mathematical Society
Representation Theory. An Electronic Journal of the American Mathematical Society, 2021, 25, pp.935-974. ⟨10.1090/ert/584⟩
Representation Theory. An Electronic Journal of the American Mathematical Society, 2021, 25, pp.935-974. ⟨10.1090/ert/584⟩
Let $G$ be a reductive algebraic group and let $Z$ be the stabilizer of a nilpotent element $e$ of the Lie algebra of $G$. We consider the action of $Z$ on the flag variety of $G$, and we focus on the case where this action has a finite number of orb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::56b625770bb99eb93853c141259287d3
https://hal.archives-ouvertes.fr/hal-02940897
https://hal.archives-ouvertes.fr/hal-02940897
Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc8ed684eafe9f62570d50158326d01b
http://arxiv.org/abs/2002.05468
http://arxiv.org/abs/2002.05468
Autor:
Thomas Gobet, Barbara Baumeister
Publikováno v:
Bulletin of the London Mathematical Society. 49:1048-1065
We show that the simple elements of the dual Garside structure of an Artin group of type $D_n$ are Mikado braids, giving a positive answer to a conjecture of Digne and the second author. To this end, we use an embedding of the Artin group of type $D_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fffbdf9c960822e52539e1f8e576f40b
https://doi.org/10.1112/blms.12100
https://doi.org/10.1112/blms.12100
Autor:
François Digne, Thomas Gobet
Publikováno v:
Mathematische Zeitschrift. 285:215-238
We study the rational permutation braids, that is the elements of an Artin-Tits group of spherical type which can be written $x^{-1} y$ where $x$ and $y$ are prefixes of the Garside element of the braid monoid. We give a geometric characterization of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6ddf84f7efd188dc187f83d061468ec2
https://doi.org/10.1007/s00209-016-1704-z
https://doi.org/10.1007/s00209-016-1704-z
Autor:
Thomas Gobet, Nathan Williams
Publikováno v:
European Journal of Combinatorics. 53:8-34
We prove that the restriction of Bruhat order to type A noncrossing partitions for the Coxeter element c = s 1 s 2 ? s n defines a distributive lattice isomorphic to the order ideals of the root poset ordered by inclusion. Motivated by the base chang
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::62400c3c0db8252b13e078aec207fd74
https://doi.org/10.1016/j.ejc.2015.10.007
https://doi.org/10.1016/j.ejc.2015.10.007
Autor:
Thomas Gobet
In Artin-Tits groups attached to Coxeter groups of spherical type, we give a combinatorial formula to express the simple elements of the dual braid monoids in the classical Artin generators. Every simple dual braid is obtained by lifting an $S$-reduc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e4466e8df1357ce77ce1ddb9bf73fa8b
Autor:
Anne-Laure Thiel, Thomas Gobet
Publikováno v:
Mathematische Zeitschrift
Mathematische Zeitschrift, Springer, In press, ⟨10.1007/s00209-019-02358-x⟩
Mathematische Zeitschrift, Springer, In press, ⟨10.1007/s00209-019-02358-x⟩
We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by generators an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd1e1476bc8b4b0e871533c326c570bf
Autor:
Thomas Gobet
Publikováno v:
Journal of Algebra. 419:277-317
We categorify the Temperley–Lieb algebra by analogues of Soergel bimodules. The key point is that the product of bimodules is not given by a usual tensor product but by a slightly more complicated operation.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7f8638a3aef9a9b00c219d365eb31412
https://doi.org/10.1016/j.jalgebra.2014.07.019
https://doi.org/10.1016/j.jalgebra.2014.07.019