Understanding the genomic basis of adaptative intraspecific phenotypic variation is a central goal in conservation genetics and evolutionary biology. Lake trout (Salvelinus namaycush) are an excellent species for addressing the genetic basis for adaptive variation because they express a striking degree of ecophenotypic variation across their range; however, necessary genomic resources are lacking. Here we utilize recently-developed analytical methods and sequencing technologies to (1) construct a high-density linkage and centromere map for lake trout, (2) identify loci underlying variation in traits that differentiate lake trout ecophenotypes and populations, (3) determine the location of the lake trout sex determination locus, and (4) identify chromosomal homologies between lake trout and other salmonids of varying divergence. The resulting linkage map contains 15,740 single nucleotide polymorphisms (SNPs) mapped to 42 linkage groups, likely representing the 42 lake trout chromosomes. Female and male linkage group lengths ranged from 43.07 to 134.64 centimorgans, and 1.97 to 92.87 centimorgans, respectively. We improved the map by determining coordinates for 41 of 42 centromeres, resulting in a map with 8 metacentric chromosomes and 34 acrocentric or telocentric chromosomes. We use the map to localize the sex determination locus and multiple quantitative trait loci (QTL) associated with intraspecific phenotypic divergence including traits related to growth and body condition, patterns of skin pigmentation, and two composite geomorphometric variables quantifying body shape. Two QTL for the presence of vermiculations and spots mapped with high certainty to an arm of linkage group Sna3, growth related traits mapped to two QTL on linkage groups Sna1 and Sna12, and putative body shape QTL were detected on six separate linkage groups. The sex determination locus was mapped to Sna4 with high confidence. Synteny analysis revealed that lake trout and congener Arctic char (Salvelinus alpinus) are likely differentiated by three or four chromosomal fissions, possibly one chromosomal fusion, and 6 or more large inversions. Combining centromere mapping information with putative inversion coordinates revealed that the majority of detected inversions differentiating lake trout from other salmonids are pericentric and located on acrocentric and telocentric linkage groups. Our results suggest that speciation and adaptive divergence within the genus Salvelinus may have been associated with multiple pericentric inversions occurring primarily on acrocentric and telocentric chromosomes. The linkage map presented here will be a critical resource for advancing conservation oriented genomic research on lake trout and exploring chromosomal evolution within and between salmonid species.