Low energy π emission in hypernuclear weak decays is studied in the soft pion limit. It is found that the π decay amplitude is dominated by the ∆I = 3/2 part of nonmesonic weak decays according to the soft pion theorem. The ratios, R(π/soft π−), for light hypernuclei are estimated in the direct quark mechanism, which predicts violation of the ∆I = 1/2 rule, and found to be about 1/3 for 4ΛHe. ∗...

Let K be an algebraic number field, and π = ⊗πv an irreducible, automorphic, cuspidal representation of GLm(AK) with analytic conductor C(π). The theorem on analytic strong multiplicity one established in this note states, essentially, that there exists a positive constant c depending on ε > 0,m, and K only, such that π can be decided completely by its local components πv with norm N(v) < c · C...

The classical detection theorem for finite groups (due to D. Quillen [Q] and B. Venkov [Q-V]) tells that if π is a finite group and Λ is a Z/p[π]-algebra then a cohomology class z ∈ H(π,Λ) is nilpotent iff for every elementary abelian psubgroup i : π0 →֒ π the restriction i (z) ∈ H(π0,Λ) of z to π0 is nilpotent. This theorem is very useful for the identification of the support variety of the gro...

Combinatorics of complexes plays an important role in topology, nonlinear analysis, game theory, and mathematical economics. In 1967, Ky Fan used door-to-door principle to prove a combinatorial Stokes’ theorem on pseudomanifolds. In 1993, Shih and Lee developed the geometric context of general position maps, π-balanced and π-subbalanced sets and used them to prove a combinatorial formula for mu...

Low energy π emission in hypernuclear weak decays is related to ∆I = 3/2 part of nonmesonic weak decays according to the soft pion theorem. We show that neither meson exchange pictures nor virtual Σ excitation can solve the π emission puzzle. On the other hand, the direct quark mechanism gives the ratio R(π/π : S-wave, soft pion) ≈ 1/4 for 4ΛHe and 5ΛHe. ∗email: [email protected]

Let D be a division algebra for a non-Archimedean local field. Given an irreducible representation π of GL2(D), we describe its restriction to the diagonal subgroup D∗ × D∗. The description is in terms of the structure of the twisted Jacquet module of the representation π. The proof involves Kirillov theory that we have developed earlier in joint work with Dipendra Prasad. The main result on re...

We show that many theorems which assert that two kinds of partitions of the same integer n are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics X and Y that have identical distribution functions. The method is an extension of the principle of sieve-equivalence, and it yields simple criteria under which we can...

(4.) Note that in Theorem 5.4, the case where A is trivial [i.e., is equal to the anabelioid associated to the trivial group {1}] is not excluded. Thus, suppose that, in Theorem 5.4, we assume further that A is trivial. Then let us observe that this implies that the underlying graph of G [orH] consists of a single vertex and no edges. [Indeed, if the underlying graph of G has at least one edge,...

Let X be a projective geometrically irreducible non-singular algebraic curve defined over a finite field Fq2 of order q . If the number of Fq2 -rational points of X satisfies the Hasse-Weil upper bound, then X is said to be Fq2 -maximal. For a point P0 ∈ X (Fq2 ), let π be the morphism arising from the linear series D := |(q + 1)P0|, and let N := dim(D). It is known that N ≥ 2 and that π is ind...