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Perfect bases in representation theory: three mountains and their springs. (English) Zbl 07822643

Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 4. Sections 5–8. Berlin: European Mathematical Society (EMS). 2976-2996 (2023).

Reviewer: Chao-Ping Dong (Changsha)

MSC: 22E46 14M15 16G20 13F60 05E10

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Bai, Roger; Dranowski, Anne; Kamnitzer, Joel

Computing fusion products of MV cycles using the Mirković-Vybornov isomorphism. (English) Zbl 1519.14046

J. Comb. Algebra 7, No. 1, 83-126 (2023).

Reviewer: Mee Seong Im (Annapolis)

MSC: 14M15 22E57 14D06 17B37 13F60

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Kamnitzer, Joel

Symplectic resolutions, symplectic duality, and Coulomb branches. (English) Zbl 1531.16013

Bull. Lond. Math. Soc. 54, No. 5, 1515-1551 (2022).

Reviewer: Mee Seong Im (Annapolis)

MSC: 16G99 17B20

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Kamnitzer, Joel; Pham, Khoa; Weekes, Alex

Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians. (English) Zbl 1484.14095

Adv. Math. 399, Article ID 108281, 52 p. (2022).

Reviewer: Mee Seong Im (Annapolis)

MSC: 14M15

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Baumann, Pierre; Kamnitzer, Joel; Knutson, Allen

The Mirković-Vilonen basis and Duistermaat-Heckman measures. (English) Zbl 1495.22011

Acta Math. 227, No. 1, 1-101 (2021).

Reviewer: Salah Mehdi (Metz)

MSC: 22E57 14D24 14M15 17B37 20G20

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Kamnitzer, Joel; McBreen, Michael; Proudfoot, Nicholas

The quantum Hikita conjecture. (English) Zbl 1498.14140

Adv. Math. 390, Article ID 107947, 53 p. (2021).

MSC: 14N35 14F10 16E05 16E40 16S38 17B10 53C26 14C05 14M15 14J42

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Cautis, Sabin; Dodd, Christopher; Kamnitzer, Joel

Associated graded of Hodge modules and categorical \(\mathfrak{sl}_2\) actions. (English) Zbl 1464.32045

Sel. Math., New Ser. 27, No. 2, Paper No. 22, 55 p. (2021).

MSC: 32S35 14M15 17B37

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Kamnitzer, Joel; Tingley, Peter; Webster, Ben; Weekes, Alex; Yacobi, Oded

On category \(\mathcal O\) for affine Grassmannian slices and categorified tensor products. (English) Zbl 1451.14143

Proc. Lond. Math. Soc. (3) 119, No. 5, 1179-1233 (2019).

MSC: 14M15 20G42 17B37

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Kamnitzer, Joel; Muthiah, Dinakar; Weekes, Alex

On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian. (English) Zbl 1423.14277

Transform. Groups 23, No. 3, 707-722 (2018).

MSC: 14M15 14N15 20G44

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Finkelberg, Michael; Kamnitzer, Joel; Pham, Khoa; Rybnikov, Leonid; Weekes, Alex

Comultiplication for shifted Yangians and quantum open Toda lattice. (English) Zbl 1384.81045

Adv. Math. 327, 349-389 (2018).

MSC: 81R12 81S10 81Q10 82C10 14M15 14N35 53D45 53D12 37K10

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Kamnitzer, Joel; Muthiah, Dinakar; Weekes, Alex; Yacobi, Oded

Reducedness of affine Grassmannian slices in type A. (English) Zbl 1379.22019

Proc. Am. Math. Soc. 146, No. 2, 861-874 (2018).

Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale)

MSC: 22E67 14M15

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Cautis, Sabin; Kamnitzer, Joel

Knot homology via derived categories of coherent sheaves. IV: Coloured links. (English) Zbl 1378.14011

Quantum Topol. 8, No. 2, 381-411 (2017).

MSC: 14F05 57M27 18D05 18F30 55N22 18E30 14M15

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Kamnitzer, Joel

A combinatorial geometric Satake equivalence. (English) Zbl 1375.14051

Adv. Math. 300, 5-16 (2016).

MSC: 14D24 14M15 14F05 17B37 18D10 20G05

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Kamnitzer, Joel; Webster, Ben; Weekes, Alex; Yacobi, Oded

Yangians and quantizations of slices in the affine Grassmannian. (English) Zbl 1325.14068

Algebra Number Theory 8, No. 4, 857-893 (2014).

Reviewer: Alessandro Ruzzi (Roma)

MSC: 14M15 14D24 53D55

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Cautis, Sabin; Kamnitzer, Joel; Licata, Anthony

Derived equivalences for cotangent bundles of Grassmannians via categorical \(\mathfrak{sl}_2\) actions. (English) Zbl 1282.14034

J. Reine Angew. Math. 675, 53-99 (2013).

Reviewer: Dragos Deliu (Wien)

MSC: 14F05 18E30 14M15 17B37

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Cautis, Sabin; Kamnitzer, Joel

Braiding via geometric Lie algebra actions. (English) Zbl 1249.14005

Compos. Math. 148, No. 2, 464-506 (2012).

Reviewer: Nicolás Andruskiewitsch (Cordoba)

MSC: 14F05 14M15 18F99

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Kamnitzer, Joel

The Beilinson-Drinfeld Grassmannian and symplectic knot homology. (English) Zbl 1230.14072

Ellwood, David A. (ed.) et al., Grassmannians, moduli spaces and vector bundles. Clay Mathematics Institute workshop on moduli spaces of vector bundles, with a view towards coherent sheaves, Cambridge, MA, USA, October 6–11, 2006. Providence, RI: American Mathematical Society (AMS); Cambridge, MA: Clay Mathematics Institute (ISBN 978-0-8218-5205-7/pbk). Clay Mathematics Proceedings 14, 81-94 (2011).

Reviewer: Sergiy Koshkin (Houston)

MSC: 14M15 57M27

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Kamnitzer, Joel

Mirković-Vilonen cycles and polytopes. (English) Zbl 1271.20058

Ann. Math. (2) 171, No. 1, 245-294 (2010).

MSC: 20G05 14M15 20G10 05E10 17B10 52B20 22E46

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Cautis, Sabin; Kamnitzer, Joel

Knot homology via derived categories of coherent sheaves. I: The \(\mathfrak{sl}(2)\)-case. (English) Zbl 1145.14016

Duke Math. J. 142, No. 3, 511-588 (2008).

Reviewer: Rina Anno (Chicago)

MSC: 14F05 57M27 18D05 18F30 55N22 18E30 14M15

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Kamnitzer, Joel

Hives and the fibres of the convolution morphism. (English) Zbl 1189.20040

Sel. Math., New Ser. 13, No. 3, 483-496 (2007).

MSC: 20G05 14M15 17B10 14L35 05E10 05E15

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Kamnitzer, Joel

The crystal structure on the set of Mirković-Vilonen polytopes. (English) Zbl 1134.14028

Adv. Math. 215, No. 1, 66-93 (2007).

Reviewer: Vladimir L. Popov (Moskva)

MSC: 14M15 17B10 17B37 20G05 14L35 20G10

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Found 21 Documents (Results 1–21)

Perfect bases in representation theory: three mountains and their springs. (English) Zbl 07822643

Computing fusion products of MV cycles using the Mirković-Vybornov isomorphism. (English) Zbl 1519.14046

Symplectic resolutions, symplectic duality, and Coulomb branches. (English) Zbl 1531.16013

Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians. (English) Zbl 1484.14095

The Mirković-Vilonen basis and Duistermaat-Heckman measures. (English) Zbl 1495.22011

The quantum Hikita conjecture. (English) Zbl 1498.14140

Associated graded of Hodge modules and categorical \(\mathfrak{sl}_2\) actions. (English) Zbl 1464.32045

On category \(\mathcal O\) for affine Grassmannian slices and categorified tensor products. (English) Zbl 1451.14143

On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian. (English) Zbl 1423.14277

Comultiplication for shifted Yangians and quantum open Toda lattice. (English) Zbl 1384.81045

Reducedness of affine Grassmannian slices in type A. (English) Zbl 1379.22019

Knot homology via derived categories of coherent sheaves. IV: Coloured links. (English) Zbl 1378.14011

A combinatorial geometric Satake equivalence. (English) Zbl 1375.14051

Yangians and quantizations of slices in the affine Grassmannian. (English) Zbl 1325.14068

Derived equivalences for cotangent bundles of Grassmannians via categorical \(\mathfrak{sl}_2\) actions. (English) Zbl 1282.14034

Braiding via geometric Lie algebra actions. (English) Zbl 1249.14005

The Beilinson-Drinfeld Grassmannian and symplectic knot homology. (English) Zbl 1230.14072

Mirković-Vilonen cycles and polytopes. (English) Zbl 1271.20058

Knot homology via derived categories of coherent sheaves. I: The \(\mathfrak{sl}(2)\)-case. (English) Zbl 1145.14016

Hives and the fibres of the convolution morphism. (English) Zbl 1189.20040

The crystal structure on the set of Mirković-Vilonen polytopes. (English) Zbl 1134.14028

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