We study the tropicalization of symplectic flag varieties with respect to the Plücker embedding. We identify a particular maximal prime cone in this tropicalization by explicitly giving its facets. For every interior point of this maximal cone, the corresponding Gröbner degeneration is the toric variety associated to the Feigin-Fourier-Littelmann-Vinberg (FFLV) polytope. Our main tool is the notion of birational sequences introduced by Fourier, Littelmann and the second author, which bridges between weighted PBW filtrations of representations of symplectic Lie algebras and degree functions on defining ideals of symplectic flag varieties.
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Keywords: Tropicalization, Gröbner degeneration, birational sequences, weighted PBW filtration, Lie algebras
Balla, George 1; Fang, Xin 1
@article{ALCO_2024__7_3_773_0, author = {Balla, George and Fang, Xin}, title = {Tropical symplectic flag varieties: a {Lie} theoretic approach}, journal = {Algebraic Combinatorics}, pages = {773--799}, publisher = {The Combinatorics Consortium}, volume = {7}, number = {3}, year = {2024}, doi = {10.5802/alco.350}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.350/} }
TY - JOUR AU - Balla, George AU - Fang, Xin TI - Tropical symplectic flag varieties: a Lie theoretic approach JO - Algebraic Combinatorics PY - 2024 SP - 773 EP - 799 VL - 7 IS - 3 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.350/ DO - 10.5802/alco.350 LA - en ID - ALCO_2024__7_3_773_0 ER -
%0 Journal Article %A Balla, George %A Fang, Xin %T Tropical symplectic flag varieties: a Lie theoretic approach %J Algebraic Combinatorics %D 2024 %P 773-799 %V 7 %N 3 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.350/ %R 10.5802/alco.350 %G en %F ALCO_2024__7_3_773_0
Balla, George; Fang, Xin. Tropical symplectic flag varieties: a Lie theoretic approach. Algebraic Combinatorics, Volume 7 (2024) no. 3, pp. 773-799. doi : 10.5802/alco.350. https://alco.centre-mersenne.org/articles/10.5802/alco.350/
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