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Item Details
| Title:
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EXTENDED GRAPHICAL CALCULUS FOR CATEGORIFIED QUANTUM SL(2)
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| By: |
Mikhail Khovanov, Aaron D. Lauda, Marco Mackaay |
| Format: |
Paperback |
| List price:
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£63.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
082188977X |
| ISBN 13: |
9780821889770 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 August, 2012 |
| Series: |
Memoirs of the American Mathematical Society 219, 1029 |
| Pages: |
87 |
| Description: |
A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in a paper (arXiv:0803.3652) by Aaron D. Lauda. Here the authors enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions. |
| Synopsis: |
A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in a paper (arXiv:0803.3652) by Aaron D. Lauda. Here the authors enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions. They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical basis elements. These formulas have integral coefficients and imply that one of the main results of Lauda's paper--identification of the Grothendieck ring of his 2-category with the idempotented quantum sl(2)--also holds when the 2-category is defined over the ring of integers rather than over a field. A new diagrammatic description of Schur functions is also given and it is shown that the the Jacobi-Trudy formulas for the decomposition of Schur functions into elementary or complete symmetric functions follows from the diagrammatic relations for categorified quantum sl(2). |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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