I suppose you could, just as long as you don't talk too much about the overall international geopolitical situation besides givens like India usurping western Europe as Capital's heart (and Brazil just being a third wheel as ever).
Alright, I'll try. You did a fine introduction earlier, so I'll skip to the political parties.:
Indian National Congress
Originally the main purveyors of the independence movement, after dominionization, the Indian National Congress soon became more concerned with more autonomy within the AFS Commonwealth, joining the People's Alliance to ensure that Indian interests are properly represented. At first, it was one of the more left-leaning of the PA cadet parties, even going through conflict with the main PA. However, after the '79 Crisis, the party underwent a rightward shift. The left dwindled, as they were expelled from the party, and a new influx of members belonging to the RSS and other Hindu nationalist parties replaced them. These new members adopted a hardline anti-Communist, pro-capitalist stance, ensuring India remained firmly in the Capitalist sphere. Their policies helped transform India into the beating heart of the capitalist sphere, surpassing even Western Europe and the main Franco-British Union. However, even in this new capitalist leader, there are systemic problems of poverty, corruption, persistence of the caste system, environmental degradation, and ethnic nationalism, which threatens to shake the INC rule, and destroy capitalism's last hope. Despite ramblings that capitalism in India is on the decline, reformists hope to solve the systemic problems of India, while maintaining its status as the rising leader of capital.
The current leader of the party, and the Prime Minister of the Greater Indian Commonwealth, is Narendra Modi, the latest in a line of RSS members in charge of the party. Despite his heavy anti-Communist stance, he has expressed his desire for reforming the system in order for India to survive in a modern world.
All-India Muslim League
Founded in 1906, the All-India Muslim League is the main political party for the Muslim minority. After spending the 1930's advocating a separate Muslim state in Muslim majority areas, negotiations between Congress head B.R. Ambedkar and party head Muhammad Ali Jinnah eventually forced the League to abandon this notion. They instead returned to their roots as a Muslim advocacy group, going into coalition with the INC to ensure that the Commonwealth recognize Muslim interests and rights. However, with the rise of the RSS as a major faction in the INC, there was growing anti-Islamic rhetoric in the Congress Party, forcing the League has since cut off its alliance, and became a major regional force in its own right. While still being pro-capitalist, it advocates more for Muslim nationalism and autonomy, which does lend itself to an anti-Communist stance, which precludes the possibility of the League joining with the Socialists and Communists in their reformist agenda. While the reactionary portion of the party has begun to return to Sir Muhammad's Iqbal's idea of a separate Islamic state, the mainstream realize that remaining part of India is in their best interest, primarily because the proposed state would be split between two sides of the country. Support largely centers around Muslim majority areas, such as the Northwest regions (Punjab, Sindh, Balochistan) and the Bengali states.
The current party head is Newaz Sharif of Punjab.
Indian Socialist Congress
Founded by dissident factions of the Indian National Congress after the founding of the Commonwealth, the Socialist Congress has taken up the mantle of full-on independence from the FBU and the AFS, albeit through legal, not revolutionary, means. It follows the Nehru style Fabian Socialist model in this respect. Through several common goals with the INC, they had managed to hold some influence in the country, helped by its moderate stance. However, this ended after 1979, when socialist politicians were arrested and/or persecuted, forcing them from office in many cases. This struck a blow to the party. However, it was able to recover, once again because it had largely absorbed the left of the Congress Party. In recent years, the Socialists have begun to advocate a reformist agenda, which includes moderate socialism, Dalit rights, and environmentalism. They are against the aggressive stance that India has taken against communism in the Indian Ocean. These stances, along with a calculated media image, became popular with a new generation of people, who are tired of capitalism, and want India to move away from dying ideologies.
The current head of the Party is Rahul Gandhi, great-grandson of Jawaharal Nehru, one of the founders of the Indian Socialist Congress.
The Worker's Communist Party of India
Originally simply "The Communist Party of India", it was founded in 1920. Originally following Marxist-Leninism, the party was significantly changed by the joining of radical Bhagat Singh in 1947, who brought the party more to a Marxist-Deleonist and Trotskyist model. The name change was meant to reflect the "Worker's Communist Party of America." They joined Comintern as a party, and became part of the pro-American faction of the alliance. It was one of the only Communist parties to remain relatively above ground in the AFS during the entirety of the Cold War, despite it adopting militant tactics at times during its history. Even during the Emergency period, they avoided an outright ban, though it was heavily persecuted during that time. After the anti-communist hysteria died down, The Communist Party moderated some of its militancy, and following their colleagues in ESCI, formed a leftist coalition with the Socialist Congress to enact a reformist agenda, sharing common goals, including the elimination of the caste system and environmentalism. Together, they hope to create a socialist state in India slowly and peacefully. Historically, it has been successful in the South, particularly in Kerala.
The current leader of the Worker's Communist Party is Sitram Yechury, a former student organizer, and later major party member. The party is considered far-left, according to Communist International
The Communist Party of India (Zapatismo)
Formed from a split in the Worker's Communist Party in 1964, it was initially a very small faction, advocating Zapatismo, peasant led revolution. However, after the moderation of the main Communist party, support had grown for this faction. It is the dissident from the "Left Consensus", desiring to advocate change more forcefully. While not resorting to outright terrorism and (very carefully) avoid outright advocating the overthrow of the government , they often organize armed strikes in rural communities, causing friction with the government. Besides this, they also organize schools and literacy programs in these communities, teaching them the tenants of communism and the evils of the caste system. This party has become very popular on college campuses, where their symbol is often plastered on walls, despite the attempts of school officials. They also protest militarism, and openly support various Communist movements in the Indian Ocean. It is not a member of Comintern, and is against both American and Soviet communism.
The current head is Muppalla Lakshmana Rao, a former radical.