Related papers: Jacobi-Trudi Identity in Super Chern-Simons Matrix…
We propose a new family of matrix models whose 1/N expansion captures the all-genus topological string on toric Calabi-Yau threefolds. These matrix models are constructed from the trace class operators appearing in the quantization of the…
In this paper we derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi's 4 and 8 squares identities to 4n^2 or 4n(n+1) squares, respectively, without using…
Integral identities for Macdonald polynomials play an important role in modern mathematics and mathematical physics. Especially interesting are the Cherednik-Macdonald-Mehta (CMM) identities, with profound connections to Double Affine Hecke…
In their study of characters of minimal affinizations of representations of orthogonal and symplectic Lie algebras, Chari and Greenstein conjectured that certain Jacobi-Trudi determinants satisfy an alternating sum formula. In this note, we…
We prove a special case of a conjecture of Davison which pertains to superpotential descriptions of fundamental group algebras $k[\pi_1(X)]$. We consider the case in which the manifold $X$ is the mapping torus $M_{g, \varphi}$ of a genus…
We consider compactifications of the matrix model of M-theory on $S^1/Z_2\times T^d$ for $d>0$, and interpret them as orbifolds of the supersymmetric U(N) Yang-Mills theory on $R\times T^{d+1}$. The orbifold group acts both on the gauge…
There are many families of functions on partitions, such as the shifted symmetric functions, for which the corresponding q-brackets are quasimodular forms. We extend these families so that the corresponding q-brackets are quasimodular for a…
We introduce a deformation of Cayley's second hyperdeterminant for even-dimensional hypermatrices. As an application, we formulate a generalization of the Jacobi-Trudi formula for Macdonald functions of rectangular shapes generalizing…
Chern-Simons theory on a U(1) bundle over a Riemann surface \Sigma_g of genus g is dimensionally reduced to BF theory with a mass term, which is equivalent to the two-dimensional Yang-Mills on \Sigma_g. We show that the former is inversely…
Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the S-matrix is constructed and seen to be formally the same as that of spinor quantum…
We consider an open string version of the topological twist previously proposed for sigma-models with G2 target spaces. We determine the cohomology of open strings states and relate these to geometric deformations of calibrated submanifolds…
We give a new Jacobi--Trudi-type formula for characters of finite-dimensional irreducible representations in type $C_n$ using characters of the fundamental representations and non-intersecting lattice paths. We give equivalent determinant…
Three-dimensional conformal theories with six supersymmetries and SU(4) R-symmetry describing stacks of M2-branes are here proposed to be related to generalized Jordan triple systems. Writing the four-index structure constants in an…
We show that the $D=11$ Supermembrane theory (M2-brane) compactified on a $M_9 \times T^2$ target space, with constant fluxes $C_{\pm}$ naturally incorporates the geometrical structure of a twisted torus. We extend the M2-brane theory to a…
The work of Andrews and Merca on the truncated Euler's pentagonal number theorem led to a resurgence in research on truncated theta series identities. In particular, Yee proved a truncated version of the Jacobi Triple Product (JTP)…
Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical…
We analyse the 4-dimensional effective supergravity theories obtained from the Scherk--Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes. We implement the appropriate orbifold projection that preserves a…
The Green functions of the Chern-Simons theory quantized in the axial gauge are shown to be calculable as the unique, exact solution of the Ward identities which express the invariance of the theory under the topological supersymmetry of…
A typical example of superintegrability is provided by expression of the Hopf link hyperpolynomial in an arbitrary representation through a pair of the Macdonald polynomials at special points. In the simpler case of the Hopf link HOMFLY-PT…
We derive 4-dimensional N=4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group U(N)^{2n}. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling…