C. Lenart
SUNY: University at Albany, Mathematics and Statistics, Faculty Member
Quantum K-theory is a K-theoretic version of quantum cohomology, which was recently defined by Y.-P. Lee. Based on a presentation for the quantum K-theory of the classical flag variety Fl_n, we define and study quantum Grothendieck... more
Quantum K-theory is a K-theoretic version of quantum cohomology, which was recently defined by Y.-P. Lee. Based on a presentation for the quantum K-theory of the classical flag variety Fl_n, we define and study quantum Grothendieck polynomials. We conjecture that they represent Schubert classes (i.e., the natural basis elements) in the quantum K-theory of Fl_n, and present strong evidence for this conjecture. We describe an efficient algorithm which, if the conjecture is true, computes the quantum K-invariants of Gromov-Witten type for Fl_n. Two explicit constructions for quantum Grothendieck polynomials are presented. The natural generalizations of several properties of Grothendieck polynomials and of the quantum Schubert polynomials due to Fomin, Gelfand, and Postnikov are proved for our quantum Grothendieck polynomials. For instance, we use a quantization map satisfying a factorization property similar to the cohomology quantization map, and we derive a Monk-type multiplication f...
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Abstract. We give an explicit combinatorial Chevalley-type formula for the equivariant K-theory of generalized flag varieties G/P which is a direct generalization of the classical Chevalley formula. Our formula implies a simple... more
Abstract. We give an explicit combinatorial Chevalley-type formula for the equivariant K-theory of generalized flag varieties G/P which is a direct generalization of the classical Chevalley formula. Our formula implies a simple combinatorial model for the characters of the ...
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... ELSEVIERDiscrete Mathematics 180 (1998) 255-280DISCRETEMATHEMATICSHopf algebras of set systemsCristian Lenarta'*, Nigel Rayba Department of Mathematics, Massachusetts ... 16], and one of our purposes here is to extendthe... more
... ELSEVIERDiscrete Mathematics 180 (1998) 255-280DISCRETEMATHEMATICSHopf algebras of set systemsCristian Lenarta'*, Nigel Rayba Department of Mathematics, Massachusetts ... 16], and one of our purposes here is to extendthe constructions therein to a richer and more ...
Research Interests:
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In this paper we study Grothendieck polynomials indexed by Grassmannian permutations, which are representatives for the classes corresponding to the structure sheaves of Schubert varieties in the K-theory of Grassmannians. These... more
In this paper we study Grothendieck polynomials indexed by Grassmannian permutations, which are representatives for the classes corresponding to the structure sheaves of Schubert varieties in the K-theory of Grassmannians. These Grothendieck polynomials are nonhomogeneous symmetric polynomials whose lowest homogeneous component is a Schur polynomial. Our treatment, which is closely related to the theory of Schur functions, gives new information
Research Interests:
... ELSEVIERDiscrete Mathematics 180 (1998) 255-280DISCRETEMATHEMATICSHopf algebras of set systemsCristian Lenarta'*, Nigel Rayba Department of Mathematics, Massachusetts ... 16], and one of our purposes here is to extendthe... more
... ELSEVIERDiscrete Mathematics 180 (1998) 255-280DISCRETEMATHEMATICSHopf algebras of set systemsCristian Lenarta'*, Nigel Rayba Department of Mathematics, Massachusetts ... 16], and one of our purposes here is to extendthe constructions therein to a richer and more ...