TAME PRINJECTIVE TYPE AND TITS FORM OF 2-PEAK POSET-I

The main aim of this paper is to give a simple criterion for a finite poset I with two maximal elements to have the category I-spr of socle projective representations of tame representation type. Our main resul t is Theorem 1 which asserts that for any upper chain reducible poset I with two maximal elements (see Definition 8) the category I-spr is o f tame representation type if and only if the Tits quadratic form q(1) : Q(1) --> Q (1.1) of I is weakly non-negative, or equivalently, if an d only if I does not contain as a peak subposet any of the one-peak po sets N-1,...,N-6* of Nazarova presented in Theorem 1 or any of the 41 two-peak posets listed in Table 1.