Related papers: Moonshine for Rudvalis's sporadic group I
We use uniqueness of a VOA (vertex operator algebra) extension of $(V_{EE_8}^+)^3$ to a Moonshine type VOA to give a new existence proof of a finite simple group of Monster type. The proof is relatively direct. Our methods depend on VOA…
It is proved that a vertex operator algebra is isomorphic to the moonshine VOA of Frenkel-Lepowsky-Meurman if it satisfies certain conditions. Our two main theorems establish a weak version of the FLM uniqueness conjecture for the moonshine…
We introduce a generalization of Brauer character to allow arbitrary finite length modules over discrete valuation rings. We show that the generalized super Brauer character of Tate cohomology is a linear combination of trace functions.…
Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They…
We describe the finite subgraph $\mathfrak{M}$ of Conway's Big Picture required to describe all $171$ genus zero groups appearing in monstrous moonshine. We determine the local structure of $\mathfrak{M}$ and give a purely group-theoretic…
In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend…
The monster sporadic group is the automorphism group of a central charge $c=24$ vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its $c=24$ stress tensor $T(z)$, this theory contains many other…
In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] it is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. This model can be…
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald-Ruijsenaars operators…
By studying 2d string compactifications with half-maximal supersymmetry in a variety of duality frames, we find a natural physical setting for understanding Umbral moonshine. Near points in moduli space with enhanced gauge symmetry, we find…
In this paper, we give decompositions of the moonshine module $V^{\natural}$ with respect to subVOAs associated to extremal Type II codes over $Z_{2k}$ for an integer $k\ge2$. Those subVOAs are isomorphic to the tensor product of 24 copies…
In this work we consider an association of meromorphic Jacobi forms of half-integral index to the pure D-type cases of umbral moonshine, and solve the module problem for four of these cases by constructing vertex operator superalgebras that…
In this paper, we revisit an earlier conjecture by one of us that related conjugacy classes of $M_{12}$ to Jacobi forms of weight one and index zero. We construct Jacobi forms for all conjugacy classes of $M_{12}$ that are consistent with…
Recently, Duncan and Mack-Crane established an isomorphism, as Virasoro modules at central charges c=12, between the space of states of the Conway Moonshine Module and the space of states of a special K3 theory that was extensively studied…
Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to each conjugacy class of the largest sporadic simple group of Mathieu. We introduce a modification of this assignment, whereby weak Jacobi forms are replaced by…
This is a historical talk about the recent confluence of two lines of research in equivariant elliptic cohomology, one concerned with connected Lie groups, the other with the finite case. These themes come together in (what seems to me…
It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald-Ruijsenaars operator in infinite number of variables. The ideals of these varieties are…
In a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial…
Special conformal field theories can have symmetry groups which are interesting sporadic finite simple groups. Famous examples include the Monster symmetry group of a $c=24$ two-dimensional conformal field theory (CFT) constructed by…
Let $k$ be an arbitrary field. We construct examples of regular local $k$-algebras $R$ (of positive dimension) for which the ring of differential operators $D_k(R)$ is trivial in the sense that it contains {\it no} operators of positive…