THE HOMFLY POLYNOMIAL OF THE DECORATED HOPF LINK

By H. Morton, Sascha G. Lukac. 2001

62 citations recorded by the source corpus.

The main goal is to find the Homfly polynomial of a link formed by decorating each component of the Hopf link with the closure of a directly oriented tangle. Such decorations are spanned in the Homfly skein of the annulus by elements Qλ, depending on partitions λ. We show how the 2-variable Homfly invariant of the Hopf link arising from decorations Qλ and Qμ can be found from the Schur symmetric function sμ of an explicit power series depending on λ. We show also that the quantum invariant of the Hopf link coloured by irreducible sl(N)q modules Vλ and Vμ, which is a 1-variable specialisation of , can be expressed in terms of an N × N minor of the Vandermonde matrix (qij).

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8f25be3beab775877c6139d5b4ba86962e211f48

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In Discrete Mathematics and Combinatorics

1. Marcos Mariño
2. Amer Iqbal
3. H. Kanno
4. H. Nakajima
5. C. Vafa
6. A. Kashani-Poor
7. Mina Aganagic
8. K. Yoshioka

In Geometry and Topology

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Amer Iqbal
6. H. Kanno
7. A. Kashani-Poor
8. Pavel Putrov

Citations in the corpus

• Topological strings and Nekrasov's formulas (2003, background): “ries E(t) = 1+ P∞ n=1 ant n by replacing the generating function of the elementary symmetric polynomials P(t) = QN i=1 (1 + xit) = 1+ P∞ n=1 ent n by E(t). Then the matrix element W R1,R2 is given by [32] WR1,R2 (q) = (dimq R1)·q ℓR2/2 ·s µR2 (EµR1 (t)) , (A.4) where dimq R = Y 1≤i<j≤d(µR) [µi −µ”
• Chern-Simons theory and topological strings (2004, unknown): “36) as a rational function of q 1 2 , λ 1 2 , and it was first written down by Morton and Lukac (2003).”
• Instanton Counting and Chern-Simons Theory (2002, methodology): “This is given by [24, 25, 8] WR1R2(q) = WR1(q) qR2 Sμ2(Eμ1(t)) .”
• Lectures on instanton counting (2003, methodology): “Using the calculation by Morton-Lukac [56], Iqbal+Kashani-Poor show that the invariants of the Hopf link has the same combinatorial expression as that of F given by the localization formula [35].”
• All Loop Topological String Amplitudes from Chern-Simons Theory (2002, methodology): “More details and examples can be found in [54].”
• The Topological Vertex (2003, methodology): “More details and examples can be found in [35].”