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pro vyhledávání: '"20g43"'
By embedding the Hecke algebra $\check H_q$ of type $D$ into the Hecke algebra $H_{q,1}$ of type $B$ with unequal parameters $(q,1)$, the $q$-Schur algebras $S^\kappa_q(n,r)$ of type $D$ is naturally defined as the endomorphism algebra of the tensor
Externí odkaz:
http://arxiv.org/abs/2406.09057
Autor:
Qin, Tao
In this paper, we consider the subdivision map between two KLRW algebras of type $A^{(1)}_e$ and $A^{(1)}_{e+1}$. We show that the image of an idempotent indexed by a partition under this map is still an idempotent indexed by a partition, and give th
Externí odkaz:
http://arxiv.org/abs/2405.14175
Autor:
Cruz, Tiago, Psaroudakis, Chrysostomos
In this paper, we prove a higher dimensional version of Auslander-Iyama-Solberg correspondence. Iyama and Solberg have shown a bijection between $n$-minimal Auslander-Gorenstein algebras and $n$-precluster tilting modules. If $A$ is an $n$-minimal Au
Externí odkaz:
http://arxiv.org/abs/2405.02736
The rook monoid, also known as the symmetric inverse monoid, is the archetypal structure when it comes to extend the principle of symmetry. In this paper, we establish a Schur-Weyl duality between this monoid and an extension of the classical Schur a
Externí odkaz:
http://arxiv.org/abs/2404.01493
We prove that the q-Schur algebras of finite type introduced in [LW22] are cellular in the sense of Graham and Lehrer, which is a generalization of Geck's theorem on the cellularity of Hecke algebras of finite type. Moreover, we study special modules
Externí odkaz:
http://arxiv.org/abs/2305.14633
Autor:
Cruz, Tiago, Erdmann, Karin
Many connections and dualities in representation theory can be explained using quasi-hereditary covers in the sense of Rouquier. The concepts of relative dominant and codominant dimension with respect to a module, introduced recently by the first-nam
Externí odkaz:
http://arxiv.org/abs/2212.00099
Autor:
Cruz, Tiago
Publikováno v:
Forum of Mathematics, Sigma 12 (2024) e105
In this paper, we develop two new homological invariants called relative dominant dimension with respect to a module and relative codominant dimension with respect to a module. These are used to establish precise connections between Ringel duality, s
Externí odkaz:
http://arxiv.org/abs/2210.09344
Autor:
Cruz, Tiago
Important connections in representation theory arise from resolving a finite-dimensional algebra by an endomorphism algebra of a generator-cogenerator with finite global dimension; for instance, Auslander's correspondence, classical Schur--Weyl duali
Externí odkaz:
http://arxiv.org/abs/2208.00291
Autor:
Arkhipov, Sergey, Mazin, Mikhail
We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a "$q=0$" version of the affine quantum group of $\mathfrak{gl}_n.$ We then use the convolution product on the equivariant $K$-theory of spaces of pairs of
Externí odkaz:
http://arxiv.org/abs/2205.05184
Autor:
Mathas, Andrew, Tubbenhauer, Daniel
Publikováno v:
J. Lond. Math. Soc. (2) 107 (2023), no. 3, 1002-1044
This paper constructs homogeneous affine sandwich cellular bases of weighted KLRW algebras in types $B$, $A^{(2)}$, $D^{(2)}$. Our construction immediately gives homogeneous sandwich cellular bases for the finite dimensional quotients of these algebr
Externí odkaz:
http://arxiv.org/abs/2201.01998