Linearizing Flows and a Cohomological Interpretation of Lax Equations

1985 ◽  
Vol 107 (6) ◽  
pp. 1445 ◽  
Author(s):  
Phillip A. Griffiths
Keyword(s):  
Lax Equations ◽  
Cohomological Interpretation

scholarly journals The $Z$-Polynomial of a Matroid

10.37236/7105 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Nicholas Proudfoot ◽  
Yuan Xu ◽  
Ben Young
Keyword(s):  
Closed Formula ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Whitney Numbers ◽  
Alternating Sums ◽  
Cohomological Interpretation

We introduce the $Z$-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the $Z$-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion, obtaining a closed formula for Kazhdan-Lusztig coefficients as alternating sums of multi-indexed Whitney numbers. For realizable matroids, we give a cohomological interpretation of the $Z$-polynomial in which the symmetry is a manifestation of Poincaré duality.

scholarly journals Stäckel transform of Lax equations

2020 ◽  
Vol 145 (2) ◽  
pp. 179-196
Author(s):  
Maciej Błaszak ◽  
Krzysztof Marciniak
Keyword(s):  
Lax Equations

scholarly journals The Strict AKNS Hierarchy: Its Structure and Solutions

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
G. F. Helminck
Keyword(s):  
Commutative Algebra ◽  
Loop Space ◽  
Integrable Hierarchy ◽  
Akns Hierarchy ◽  
Zero Curvature ◽  
Lax Equations

We discuss an integrable hierarchy of compatible Lax equations that is obtained by a wider deformation of a commutative algebra in the loop space ofsl2than that in the AKNS case and whose Lax equations are based on a different decomposition of this loop space. We show the compatibility of these Lax equations and that they are equivalent to a set of zero curvature relations. We present a linearization of the system and conclude by giving a wide construction of solutions of this hierarchy.

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