http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Monoidal categories associated with strata of flag manifolds
Kashiwara, Masaki,Kim, Myungho,Oh, Se-jin,Park, Euiyong Elsevier 2018 Advances in mathematics Vol.328 No.-
<P><B>Abstract</B></P> <P>We construct a monoidal category <SUB> C w , v </SUB> which categorifies the doubly-invariant algebra C <SUP> N ′ </SUP> ( w ) <SUP> [ N ] N ( v ) </SUP> associated with Weyl group elements <I>w</I> and <I>v</I>. It gives, after a localization, the coordinate algebra C [ <SUB> R w , v </SUB> ] of the open Richardson variety associated with <I>w</I> and <I>v</I>. The category <SUB> C w , v </SUB> is realized as a subcategory of the graded module category of a quiver Hecke algebra <I>R</I>. When v = id , <SUB> C w , v </SUB> is the same as the monoidal category which provides a monoidal categorification of the quantum unipotent coordinate algebra <SUB> A q </SUB> <SUB> ( n ( w ) ) Z [ q , <SUP> q − 1 </SUP> ] </SUB> given by Kang–Kashiwara–Kim–Oh. We show that the category <SUB> C w , v </SUB> contains special determinantial modules M ( <SUB> w ≤ k </SUB> Λ , <SUB> v ≤ k </SUB> Λ ) for k = 1 , … , ℓ ( w ) , which commute with each other. When the quiver Hecke algebra <I>R</I> is symmetric, we find a formula of the degree of <I>R</I>-matrices between the determinantial modules M ( <SUB> w ≤ k </SUB> Λ , <SUB> v ≤ k </SUB> Λ ) . When it is of finite <I>ADE</I> type, we further prove that there is an equivalence of categories between <SUB> C w , v </SUB> and <SUB> C u </SUB> for w , u , v ∈ W with w = v u and ℓ ( w ) = ℓ ( v ) + ℓ ( u ) .</P>
Supercategorification of quantum Kac-Moody algebras
Kang, S.J.,Kashiwara, M.,Oh, S.j. Academic Press ; Elsevier Science B.V. Amsterdam 2013 Advances in mathematics Vol.242 No.-
We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac-Moody algebras and their integrable highest weight modules.
Geometric construction of crystal bases for quantum generalized Kac–Moody algebras
Kang, Seok-Jin,Kashiwara, Masaki,Schiffmann, Olivier Elsevier 2009 Advances in mathematics Vol.222 No.3
<P><B>Abstract</B></P><P>We provide a geometric realization of the crystal B(∞) for quantum generalized Kac–Moody algebras in terms of the irreducible components of certain Lagrangian subvarieties in the representation spaces of a quiver.</P>
Simplicity of heads and socles of tensor products
Kang, Seok-Jin,Kashiwara, Masaki,Kim, Myungho,Oh, Se-jin London Mathematical Society 2015 Compositio mathematica Vol.151 No.2
<B>Abstract</B><P>We prove that, for simple modules $M$ and $N$ over a quantum affine algebra, their tensor product $M\otimes N$ has a simple head and a simple socle if $M\otimes M$ is simple. A similar result is proved for the convolution product of simple modules over quiver Hecke algebras.</P>
Supercategorification of quantum Kac-Moody algebras II
Kang, S.J.,Kashiwara, M.,Oh, S.j. Academic Press ; Elsevier Science B.V. Amsterdam 2014 Advances in mathematics Vol.265 No.-
In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family of quantum superalgebras and their integrable highest weight modules. We show that, by taking a specialization, we obtain a supercategorification of quantum Kac-Moody superalgebras and their integrable highest weight modules.
Symmetric quiver Hecke algebras and <i>R</i>-matrices of quantum affine algebras III
Kang, Seok-Jin,Kashiwara, Masaki,Kim, Myungho,Oh, Se-jin Oxford University Press 2015 Proceedings of the London Mathematical Society Vol.111 No.2
<P>Let [Formula] be the category of finite-dimensional integrable modules over the quantum affine algebra [Formula] and let [Formula] denote the category of finite-dimensional graded modules over the quiver Hecke algebra of type [Formula]. In this paper, we investigate the relationship between the categories [Formula] and [Formula] by constructing the generalized quantum affine Schur–Weyl duality functors [Formula] from [Formula] to [Formula].</P>