Extended graphical calculus for categorified quantum sl(2) /
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| Imprint: | Providence, R.I. : American Mathematical Society, c2012. |
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| Description: | v, 87 p. : ill. ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; no. 1029 Memoirs of the American Mathematical Society ; no. 1029. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8895794 |
| Summary: | 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.<br> <br> 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). |
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| Item Description: | "September 2012, volume 219, number 1029 (second of 5 numbers)." |
| Physical Description: | v, 87 p. : ill. ; 26 cm. |
| ISBN: | 9780821889770 082188977X |
| ISSN: | 0065-9266 ; |
