23 citations · 100 across the 14 of their papers we have counts for
14 papers
Partial -invariants and cluster categorifications
Peigen Cao, Ryo Fujita, Kota Murakami
The -invariant in cluster algebras is a combinatorial invariant that unifies the -invariant from additive categorification and the -invariant from monoidal cate…
Freezing operators in representation theory of quantum loop algebras
Ryo Fujita, Fan Qin
We prove the Hernandez conjecture on the simple -characters (an analog of the Kazhdan--Lusztig conjecture) for untwisted quantum loop algebras of classical type. This result…
Inflations among quantum Grothendieck rings of type A
Ryo Fujita
We introduce a collection of injective homomorphisms among the quantum Grothendieck rings of finite-dimensional modules over the quantum loop algebras of type . In the…
Singularities of normalized R-matrices and E-invariants for Dynkin quivers
Ryo Fujita
We study the singularities of normalized R-matrices between arbitrary simple modules over the quantum loop algebra of type ADE in Hernandez--Leclerc's level-one subcategory using e…
Isomorphisms among quantum Grothendieck rings and cluster algebras
Ryo Fujita, David Hernandez, Se-jin Oh +1
We establish a cluster theoretical interpretation of the isomorphisms of [F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of representations of quantum l…
Deformed Cartan matrices and generalized preprojective algebras II: General type
Ryo Fujita, Kota Murakami
We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical interpretation by graded modules over t…
Deformed Cartan matrices and generalized preprojective algebras I: Finite type
Ryo Fujita, Kota Murakami
We give an interpretation of the -deformed Cartan matrices of finite type and their inverses in terms of bigraded modules over the generalized preprojective algebras of Lang…
Isomorphisms among quantum Grothendieck rings and propagation of positivity
Ryo Fujita, David Hernandez, Se-jin Oh +1
Let ( be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with being of simply-lace…
Q-data and representation theory of untwisted quantum affine algebras
Ryo Fujita, Se-jin Oh
For a complex finite-dimensional simple Lie algebra , we introduce the notion of Q-datum, which generalizes the notion of a Dynkin quiver with a height function from…
Graded quiver varieties and singularities of normalized R-matrices for fundamental modules
Ryo Fujita
We present a simple unified formula expressing the denominators of the normalized R-matrices between the fundamental modules over the quantum loop algebras of type ADE. It has an i…
Coherent IC-sheaves on type affine Grassmannians and dual canonical basis of affine type
Michael Finkelberg, Ryo Fujita
The convolution ring was identified with a quantum unipotent cell of the loop group in [Cautis-Williams,…
Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality
Ryo Fujita
For a Dynkin quiver of type ADE and a sum of simple roots, we construct a bimodule over the quantum loop algebra and the quiver Hecke algebra of the corresponding type via…
Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types
Ryo Fujita
For a Dynkin quiver (of type ADE), we consider a central completion of the convolution algebra of the equivariant K-group of a certain Steinberg type graded quiver variety. We…
Tilting modules of affine quasi-hereditary algebras
Ryo Fujita
We discuss tilting modules of affine quasi-hereditary algebras. We present an existence theorem of indecomposable tilting modules when the algebra has a large center and use it to…