Physical CombinatoricsMasaki Kashiwara, Tetsuji Miwa Taking into account the various criss-crossing among mathematical subject, Physical Combinatorics presents new results and exciting ideas from three viewpoints; representation theory, integrable models, and combinatorics. This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Recent developments in integrable models reveal an unexpected link between representation theory and statistical mechanics through combinatorics. |
Contents
On the Combinatorics of ForresterBaxter Models | 49 |
C¹ and A Cases | 105 |
Theta Functions Associated with Affine Root Systems and the Elliptic | 140 |
A Generalization of the qSaalschütz Sum and the Burge Transform | 163 |
The Bethe Equation at q 0 the Möbius Inversion Formula | 185 |
Hidden EType Structures in Dilute A Models | 217 |
Canonical Bases of HigherLevel qDeformed Fock Spaces | 248 |
FiniteGap Difference Operators with Elliptic Coefficients | 301 |
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Common terms and phrases
action affine affine Lie algebra analogue b₁ b₂ Bethe ansatz Bethe equation coefficients column insertion combinatorial configuration crystal bases crystal basis crystal graph D-transform define definition denote diagram dilute eigenvalue elliptic empty box energy function fermionic Fock space follows formula Hence identities implies integer interfacial irreducible Ising model isomorphism Kashiwara Kazhdan-Lusztig polynomials Knuth Kostka polynomial Lamé operator lattice Lemma Lie algebra m₁ Math matrix mi+1 module move Note obtain odd band off-diagonal solutions pair particle partition path Phys polynomials PROOF Proposition q-deformed Fock space QTMs quantum representation resp result reverse slide root systems scoring vertices Section spectral parameter string solutions T(b₁ t₁ Theorem theta functions transformation type I slide vector vertex wedge wedge product weight wt h Xi+1