ALGEBRAIC COMBINATORICS

no. 2
FFLV-type monomial bases for type B
Makhlin, Igor1
1 Skolkovo Institute of Science and Technology Center for Advanced Studies Ulitsa Nobelya 3 Moscow 121205 Russia and National Research University Higher School of Economics International Laboratory of Representation Theory and Mathematical Physics Ulitsa Usacheva 6 Moscow 119048 Russia
Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 305-322.

We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible 𝔰𝔬 2n+1 -module. These bases are in many ways similar to the FFLV bases for types A and C. They are also defined combinatorially via sums over Dyck paths in certain triangular grids. Our sums, however, involve weights depending on the length of the corresponding root. Accordingly, our bases also induce bases in certain degenerations of the modules but these degenerations are obtained not from the filtration by PBW degree but by a weighted version thereof.

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DOI: 10.5802/alco.41
Classification: 17B10, 17B20, 05E10
Keywords: Lie algebras, type B, monomial bases, FFLV bases, FFLV polytopes, PBW degenerations
Makhlin, Igor 1

1 Skolkovo Institute of Science and Technology Center for Advanced Studies Ulitsa Nobelya 3 Moscow 121205 Russia and National Research University Higher School of Economics International Laboratory of Representation Theory and Mathematical Physics Ulitsa Usacheva 6 Moscow 119048 Russia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Makhlin, Igor. FFLV-type monomial bases for type $B$. Algebraic Combinatorics, Volume 2 (2019) no. 2, pp. 305-322. doi : 10.5802/alco.41. https://alco.centre-mersenne.org/articles/10.5802/alco.41/

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