Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products

E. Cline, B. Parshall, and L. Scott, Finite-dimensional algebras and highest weight categories , J. Reine Angew. Math. 391

1988

Earlier work this paper cites.

Wolfgang Soergel, Kategorie 𝒪 \mathcal{O} , perverse Garben und Moduln über den Koinvarianten zur Weylgruppe , J. Amer. Math. Soc. 3

1990

Earlier work this paper cites.

by same author, The combinatorics of Harish-Chandra bimodules , J. Reine Angew. Math. 429

1992

Earlier work this paper cites.

George Lusztig, Introduction to quantum groups , Progress in Mathematics, vol. 110, Birkhäuser Boston Inc., Boston, MA, 1993

1993

Earlier work this paper cites.

Susumu Ariki and Kazuhiko Koike, A Hecke algebra of ( ℤ / r ​ ℤ ) ≀ 𝔖 n ({\mathbb{Z}}/r{\mathbb{Z}})\wr{\mathfrak{S}}_{n} and construction of its irreducible representations , Adv. Math. 106

1994

Earlier work this paper cites.

Susumu Ariki, On the decomposition numbers of the Hecke algebra of G ⁡ ( m , 1 , n ) G(m,1,n) , J. Math. Kyoto Univ. 36

1996

Earlier work this paper cites.

Alexander Beilinson, Victor Ginzburg, and Wolfgang Soergel, Koszul duality patterns in representation theory , J. Amer. Math. Soc. 9

1996

Earlier work this paper cites.

Edward Cline, Brian Parshall, and Leonard Scott, Stratifying endomorphism algebras , Mem. Amer. Math. Soc. 124

1996

Earlier work this paper cites.

Richard Dipper, Gordon James, and Andrew Mathas, Cyclotomic q q -Schur algebras , Math. Z. 229

1998

Earlier work this paper cites.

Victor Ginzburg, Nicolas Guay, Eric Opdam, and Raphaël Rouquier, On the category 𝒪 \mathcal{O} for rational Cherednik algebras , Invent. Math. 154

2003

Cited alongside, same era.

by same author, Category 𝒪 \mathcal{O} : quivers and endomorphism rings of projectives , Represent. Theory 7

2003

Cited alongside, same era.

Arkady Berenstein and David Kazhdan, Geometric and unipotent crystals. II. From unipotent bicrystals to crystal bases , Quantum groups, Contemp. Math., vol. 433, Amer. Math. Soc., Providence, RI, 2007, pp. 13–88

2007

Cited alongside, same era.

Joshua Sussan, Category 𝒪 \mathcal{O} and 𝔰 ​ 𝔩 ​ ( k ) \mathfrak{sl}(k) link invariants , 2007, arXiv: 0701045

2007

Cited alongside, same era.

Jonathan Brundan and Alexander Kleshchev, Schur-Weyl duality for higher levels , Selecta Math. (N.S.) 14

2008

Cited alongside, same era.

Alexander E. Hoffnung and Aaron D. Lauda, Nilpotency in type A A cyclotomic quotients , J. Algebraic Combin. 32

2010

Closest in time.

by same author, Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A A , Adv. Math. 225

2010

Closest in time.

by same author, A categorification of quantum sl ⁡ ( n ) {\rm sl}(n) , Quantum Topol. 1

2010

Closest in time.

Aaron D. Lauda, A categorification of quantum sl ⁡ ( 2 ) {\rm sl}(2) , Adv. Math. 225

2010

Closest in time.

by same author, A diagrammatic approach to categorification of quantum groups II , Trans. Amer. Math. Soc. 363

2011

Closest in time.

Alexander Kleshchev and Arun Ram, Representations of Khovanov-Lauda-Rouquier algebras and combinatorics of Lyndon words , Math. Ann. 349