Symmetric Functions Schubert Polynomials and Degeneracy Loci

By Laurent Manivel, John Swallow. 2001

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The Odd nilHecke Algebra and its Diagrammatics (2011, methodology): “By analogy with the even case [13], we define the odd nilHecke ring ONHa to be the graded unital associative ring generated by elements x1, .”
Series of Lie groups (2002, methodology): “Now we use the Littlewood-Richardson rule to compute these scalar products: we refer the reader to [18] for the statement and the terminology we use in the sequel.”
Singularities of Generalized Richardson Varieties (2010, result): “ert varieties in general position in a homogeneous variety G/P. Their cohomology classes encode information that plays a signiﬁcant role in algebraic geometry, representation theory and combinatorics [15, 16, 32, 35]. In recent years, the study of the singularities of Richardson varieties has receiv”
An introduction to diagrammatic algebra and categorified quantum sl(2) (2011, background): “The nilHecke algebra has a well documented connection to cohomology rings of flag varieties [4, 22] and is further related to the theory of Schubert varieties, see [36, 6, 45, 54].”