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We establish algebraically and geometrically a duality between the Iwahori-Hecke algebra of type D and two new quantum algebras arising from the geometry of N-step isotropic flag varieties of type D.
1972
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D. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras
1979
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A. Beilinson, J. Bernstein, P. Deligne, Faisceaux pervers
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A. Beilinson, G. Lusztig, R. McPherson, A geometric setting for the quantum deformation of G L n GL_{n}
1990
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I. Grojnowski, G. Lusztig, On bases of irreducible representations of quantum G L n GL_{n}
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V. Ginzburg and E. Vasserot, Langlands reciprocity for affine quantum groups of type A n A_{n}
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Z. Wan, Geometry of classical groups over finite fields
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R. Green, Hyperoctaheral Schur algebras
1997
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G. Lusztig, Aperiodicity in quantum affine 𝔤 𝔩 n \mathfrak{gl}_{n}
1999
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G. Lusztig, Transfer maps for quantum affine 𝔰 𝔩 n \mathfrak{sl}_{n}
2000
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O. Schiffmann and E. Vasserot, Geometric construction of the global base of the quantum modified algebra of 𝔤 𝔩 ^ n \widehat{\mathfrak{gl}}_{n}
2000
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S. Doty, A. Giaquinto, Presenting Schur algebras
2002
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G. Letzter, Coideal subalgebras and quantum symmetric pairs
2002
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A. Björner, F. Brenti, Combinatorics of Coxeter groups
2005
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G. Pouchin, A geometric Schur-Weyl duality for quotients of affine Hecke algebras,
2009
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M. Khovanov, A. Lauda, A diagrammatic approach to categorification of quantum groups III
2010
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A. Lauda, A categorification of quantum sl(2)
2010
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G. Lusztig, Introduction to Quantum groups
2010
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K. McGerty, On the geometric realization of the inner product and canonical basis for quantum affine 𝔰 𝔩 n \mathfrak{sl}_{n}
2012
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H. Bao, W. Wang, A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
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